Professor Norman Dancer

F07 - Carslaw Building
The University of Sydney

Telephone 9351 4141
Fax 9351 4534

Biographical details

Norman Dancer is a member of the Editorial Advisory Board of the book publishing program in mathematics launched jointly by de Gruyter and Versita. The program is focused on Central and Eastern Europe.

Research interests

Nonlinear analysis, especially degree theory, Morse theory and Conley index; applications to nonlinear ordinary and partial differential equations, including singular perturbations; bifurcation theory.

Norman Dancer is a member of the Nonlinear Analysis Research Group.

Teaching and supervision

Timetable

Selected grants

2017

  • Nonlinear Partial Differential equations; bubbles, layers and stability; Yan S, Dancer E, Du Y; Australian Research Council (ARC)/Discovery Projects (DP).

2013

  • Singularity, degeneracy and related problems in nonlinear partial differential equations; Yan S, Dancer E, Du Y; Australian Research Council (ARC)/Discovery Projects (DP).

2011

  • Stable and Finite Morse index solutions and peak solutions of nonlinear elliptic equations; Dancer E; Australian Research Council (ARC)/Discovery Projects (DP).

2010

  • Transitions and singular behaviour in nonlinear partial differential equations; Du Y, Dancer E, Yan S; Australian Research Council (ARC)/Discovery Projects (DP).

2008

  • Finite Morse index solutions of non-linear partial differential equations; Dancer E; Australian Research Council (ARC)/Discovery Projects (DP).

2007

  • Sharp transitions in partial differential equations and related problems; Du Y, Dancer E, Yan S; Australian Research Council (ARC)/Discovery Projects (DP).

2005

  • Joint venture between AMSI members required under Funding agreement between the Commonwealth and the; Dancer E, Taylor D, Weber N.
  • Stable and peak solutions of partial differential equations; Dancer E; Australian Research Council (ARC)/Discovery Projects (DP).

2003

  • Free boundary problems in partial differential equations and related topics; Du Y, Dancer E, Du Y; Australian Research Council (ARC)/Discovery Projects (DP).
  • Symmetry and bifurcation; Dancer E; DVC Research/Research and Development Scheme: Research and Development (R&D).

2002

  • Abstract methods for nonlinear partial differential equations; Dancer E; Australian Research Council (ARC)/Discovery Projects (DP).

2000

  • Population models and partial differential equations; Dancer E; Australian Research Council (ARC)/Large Research Grants (LRG).
  • Bifurcations and secondary bifurcations for ordinary and partial differential equations; Dancer E; Australian Research Council (ARC)/Large Research Grants (LRG).
  • The effects of the domain geometry and topology in nonlinear elliptic equations; Noussair, E, Dancer E; Australian Research Council (ARC)/Large Research Grants (LRG).

Selected publications

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Book Chapters

  • Dancer, E. (2006). Stable and not too unstable solutions on Rn for small diffusion. In Brunner H, Zhao X-Q, Zou X, (Eds.), Nonlinear dynamics and evolution equations, (pp. 67-93). Providence, Rhode Island: American Mathematical Society.

Journals

  • Dancer, E., Gladiali, F., Grossi, M. (2017). On the Hardy-Sobolev equation. Proceedings of the Royal Society of Edinburgh Section A (Mathematics), 147A, 299-336. [More Information]
  • Ackermann, N., Dancer, E. (2016). Precise exponential decay for solutions of semilinear elliptic equations and its effect on the structure of the solution set for a real analytic nonlinearity. Differential and Integral Equations, 29(7-8), 757-774.
  • Dancer, E., Daners, D., Hauer, D. (2015). A Liouville theorem for p-harmonic functions on exterior domains. Positivity, 19(3), 577-586. [More Information]
  • Daners, D., Hauer, D., Dancer, E. (2015). Uniform convergence of solutions to elliptic equations on domains with shrinking holes. Advances in Differential Equations, 20(5-6), 463-494.
  • Dancer, E. (2014). A remark on stable solutions of nonlinear elliptic equations on R3 or R4. Differential and Integral Equations, 27(5-6), 483-488.
  • Dancer, E. (2014). On the converse problem for the gross-pitaevskii equations with a large parameter. Discrete and Continuous Dynamical Systems - Series A, 34(6), 2481-2493. [More Information]
  • Dancer, E., Wang, K., Zhang, Z. (2013). Addendum to "The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture". Journal of Functional Analysis, 264(4), 1125-1129. [More Information]
  • Dancer, E. (2013). Addendum to: Stable and finite Morse index solutions for Dirichlet problems with small diffusion in a degenerate case and problems with infinite boundary values. Advanced Nonlinear Studies, 13(4), 791-794.
  • Dancer, E., Du, Y., Efendiev, M. (2013). Quasilinear Elliptic Equations on Half- and Quarter-spaces. Advanced Nonlinear Studies, 13(1), 115-136.
  • Dancer, E. (2013). Some bifurcation results for rapidly growing nonlinearities. Discrete and Continuous Dynamical Systems - Series S, 33(1), 153-161. [More Information]
  • Dancer, E., Hillman, J., Pistoia, A. (2012). Deformation retracts to the fat diagonal and applications to the existence of peak solutions of nonlinear elliptic equations. Pacific Journal of Mathematics, 256(1), 67-78. [More Information]
  • Dancer, E., Wang, K., Zhang, Z. (2012). Dynamics of strongly competing systems with many species. Transactions of the American Mathematical Society, 364(2), 961-1005. [More Information]
  • Dancer, E., Weth, T. (2012). Liouville-type results for non-cooperative elliptic systems in a half-space. Journal of The London Mathematical Society, 86(1), 111-128. [More Information]
  • Dancer, E., Guo, Z., Wei, J. (2012). Non-radial singular solutions of Lane-Emden equations in $R^N$. Indiana University Mathematics Journal, 61(5), 1971-1996. [More Information]
  • Dancer, E. (2012). On domain perturbation for super-linear Neumann problems and a question of Y. Lou, W-M Ni and L. Su. Discrete and Continuous Dynamical Systems - Series A, 32(11), 3861-3869. [More Information]
  • Dancer, E., Wang, K., Zhang, Z. (2012). The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture. Journal of Functional Analysis, 262(3), 1087-1131. [More Information]
  • Dancer, E., Santra, S., Wei, J. (2011). Asymptotic behavior of the least energy solution of a problem with competing powers. Journal of Functional Analysis, 261, 2094-2134. [More Information]
  • Crooks, E., Dancer, E. (2011). Competition Systems With Strong Interaction on a Subdomain. Topological Methods In Nonlinear Analysis, 37(1), 37-53.
  • Dancer, E., Du, Y., Guo, Z. (2011). Finite Morse index solutions of an elliptic equation with supercritical exponent. Journal of Differential Equations, 250(8), 3281-3310. [More Information]
  • Dancer, E., Santra, S., Wei, J. (2011). Least energy nodal solution of a singular perturbed problem with jumping nonlinearity. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, X(1), 19-36.
  • Dancer, E. (2011). On the least point of the spectrum of certain cooperative linear systems with a large parameter. Journal of Differential Equations, 250(1), 33-38. [More Information]
  • Dancer, E., Wang, K., Zhang, Z. (2011). Uniform Holder estimate for singularly perturbed parabolic systems of Bose-Einstein condensates and competing species. Journal of Differential Equations, 251, 2737-2769. [More Information]
  • Bartsch, T., Dancer, E., Wang, Z. (2010). A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system. Calculus of Variations and Partial Differential Equations, 37(3-4), 345-361. [More Information]
  • Dancer, E., Wei, J., Weth, T. (2010). A priori bounds versus multiple existence of positive solutions for a nonlinear Schrodinger system. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, AN 27(3), 953-969. [More Information]
  • Crooks, E., Dancer, E. (2010). Highly nonlinear large-competition limits of elliptic systems. Nonlinear Analysis, 73(5), 1447-1457. [More Information]
  • Dancer, E. (2010). New Results for Finite Morse Index Solutions on R^N and Applications. Advanced Nonlinear Studies, 10(3), 581-595. [More Information]
  • Dancer, E. (2010). Proofs of the Results in “Boundary-Value Problems for Weakly Nonlinear Ordinary Differential Equations�? Rendiconti dell' Istituto di matematica dell' Università di Trieste, 42(2010), 31-57.
  • Dancer, E., Santra, S. (2010). Singular perturbed problems in the zero mass case: asymptotic behavior of spikes. Annali di Matematica Pura ed Applicata, 189(2), 185-225. [More Information]
  • Dancer, E. (2009). A Conley Index Calculation. Bulletin of the Australian Mathematical Society, 80(3), 510-520. [More Information]
  • Dancer, E., Micheletti, A., Pistoia, A. (2009). Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian manifolds. Manuscripta Mathematica, 128(2), 163-193. [More Information]
  • Dancer, E., Farina, A. (2009). On the classification of solutions of -Delta u=e^u on R^N: stability outside a compact set and applications. Proceedings of the American Mathematical Society, 137(4), 1333-1338. [More Information]
  • Dancer, E. (2009). On the principal eigenvalue of linear cooperating elliptic systems with small diffusion. Journal of Evolution Equations, 9(3), 419-428. [More Information]
  • Dancer, E., Hilhorst, D., Yan, S. (2009). Peak solutions for the Dirichlet problem of an elliptic system. Discrete and Continuous Dynamical Systems - Series A, 24(3), 731-761. [More Information]
  • Dancer, E. (2009). Peak solutions without non-degeneracy conditions. Journal of Differential Equations, 246(8), 3077-3088. [More Information]
  • Bartsch, T., Dancer, E. (2009). Poincare-Hopf type formulas on convex sets of Banach spaces. Topological Methods In Nonlinear Analysis, 34(2), 213-229.
  • Dancer, E. (2009). Some remarks on half space problems. Discrete and Continuous Dynamical Systems - Series A, 25(1), 83-88. [More Information]
  • Dancer, E., Wei, J. (2009). Spike solutions in coupled nonlinear Schrodinger equations with attractive interaction. Transactions of the American Mathematical Society, 361(3), 1189-1208.
  • Dancer, E. (2009). Stable and finite Morse index solutions for Dirichlet problems with small diffusion in a degenerate case and problems with infinite boundary values. Advanced Nonlinear Studies, 9(4), 657-678.
  • Dancer, E., Santra, S. (2008). Existence and multiplicity of solutions for a weakly coupled radial system in a ball. Communications on Pure and Applied Analysis, 7(4), 787-793. [More Information]
  • Dancer, E. (2008). Finite Morse index solutions of exponential problems. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 25(1), 173-179. [More Information]
  • Dancer, E. (2008). Finite Morse index solutions of supercritical problems. Journal fur die Reine und Angewandte Mathematik (Crelle's journal), 620(1), 213-233. [More Information]
  • Dancer, E. (2008). Moving plane methods for systems on half spaces. Mathematische Annalen, 342, 245-254. [More Information]
  • Dancer, E., Yan, S. (2008). On the Lazer-Mckenna conjecture involving critical and supercritical exponents. Methods and Applications of Analysis, 15(1), 97-120.
  • Dancer, E., Yan, S. (2008). The Lazer-McKenna conjecture and a free boundary problem in two dimensions. Journal of The London Mathematical Society, 78(3), 639-662. [More Information]
  • Dancer, E., Yan, S. (2007). A new type of concentration solutions for a singularly perturbed elliptic problem. Transactions of the American Mathematical Society, 359(4), 1765-1790. [More Information]
  • Dancer, E. (2007). Conley indices on convex sets, attractor-repeller pairs and applications to multiple solutions of nonlinear elliptic equations. Journal of Fixed Point Theory and Applications, 1(1), 47-60. [More Information]
  • Dancer, E. (2007). Domain variation and non-uniqueness of homoclinic solutions of some partial differential equations on strips. Journal of Dynamics and Differential Equations, 19(3), 709-718. [More Information]
  • Crooks, E., Dancer, E., Hilhorst, D. (2007). Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems - Series B, 8(1), 39-44.
  • Dancer, E., Ren, X., Yan, S. (2007). On multiple radial solutions of a singularly perturbed nonlinear elliptic system. SIAM Journal On Mathematical Analysis, 38(6), 2005-2041. [More Information]
  • Dancer, E., Santra, S. (2007). On the superlinear Lazer-Mckenna conjecture: the non-homogeneous case. Advances in Differential Equations, 12(9), 961-993.
  • Dancer, E., Wei, J. (2007). Sign-changing solutions for supercritical elliptic problems in domains with small holes. Manuscripta Mathematica, 123(4), 493-511. [More Information]
  • Dancer, E. (2007). Supercritical finite Morse index solutions. Nonlinear Analysis, 66(1), 268-269. [More Information]
  • Dancer, E., Du, Y. (2006). A uniqueness theorem for a free boundary problem. Proceedings of the American Mathematical Society, 134(11), 3223-3230. [More Information]
  • Dancer, E., Yan, S. (2006). Interior peak solutions for an elliptic system of FitzHugh-Nagumo type. Journal of Differential Equations, 229(2), 654-679. [More Information]
  • Dancer, E., Yan, S. (2006). Multipeak solutions for an elliptic system of Fitzhugh-Nagumo type. Mathematische Annalen, 335(3), 527-569. [More Information]
  • Bartsch, T., Dancer, E., Peng, S. (2006). On multi-bump semi-classical bound states of nonlinear Schrodinger equations with electromagnetic fields. Advances in Differential Equations, 11(7), 781-812.
  • Dancer, E. (2006). On stable and meta-stable solutions of the shadow system for the Geirer-Meinhardt equation. Advanced Nonlinear Studies, 6(3), 483-490. [More Information]
  • Dancer, E., Yan, S. (2006). Solutions with interior and boundary peaks for the Neumann problem of an elliptic system of FitzHugh-Nagumo type. Indiana University Mathematics Journal, 55(1), 217-258. [More Information]
  • Dancer, E., Shi, J. (2006). Uniqueness and nonexistence of positive solutions to semipositone problems. Bulletin of the London Mathematical Society, 38(6), 1033-1044. [More Information]
  • Dancer, E. (2006). Weak convergence, local bifurcations and uniqueness theorems. Accademia Nazionale dei Lincei. Atti. Matematica e Applicazioni. Rendiconti, 17(3), 243-255.
  • Dancer, E., Geba, K., Rybicki, S. (2005). Classification of homotopy classes of equivariant gradient maps. Fundamenta Mathematicae, 185(1), 1-18.
  • Dancer, E., Yan, S. (2005). Multipeak solutions for the Neumann problem of an elliptic system of Fitzhugh-Nagumo type. Proceedings of the London Mathematical Society, 90(3), 209-244. [More Information]
  • Dancer, E., Yan, S. (2005). On the superlinear Lazer-McKenna conjecture. Journal of Differential Equations, 210(2), 317-351. [More Information]
  • Dancer, E., Yan, S. (2005). On the superlinear Lazer-McKenna conjecture: Part II. Communications in Partial Differential Equations, 30(9), 1331-1358. [More Information]
  • Dancer, E. (2005). Remarks on nonlinear elliptic problems on long domains. Advanced Nonlinear Studies, 5(2), 253-263.
  • Dancer, E. (2005). Some examples on solution structures for weakly nonlinear elliptic equations. Discrete and Continuous Dynamical Systems - Series A, 12(5), 817-826. [More Information]
  • Dancer, E. (2005). Stable and finite morse index solutions on Rn or on bounded domains with small diffusion. Transactions of the American Mathematical Society, 357(3), 1225-1243. [More Information]
  • Dancer, E., Yan, S. (2004). A minimization problem associated with elliptic systems of FitzHugh-Nagumo type. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 21(2), 237-253. [More Information]
  • Dancer, E., Yan, S. (2004). Construction Of Various Types Of Solutions For An Elliptic Problem. Calculus of Variations and Partial Differential Equations, 20(1), 93-118. [More Information]
  • Dancer, E. (2004). Stable and finite morse index solutions on R^n or on bounded domains with small diffusion II. Indiana University Mathematics Journal, 53(1), 97-108.
  • Dancer, E. (2004). Stable Solutions On R\Sp N And The Primary Branch Of Some Non-Self-Adjoint Convex Problems. Differential and Integral Equations, 17(9-10), 961-970.
  • Dancer, E., Du, Y., Ma, L. (2003). Asymptotic behavior of positive solutions of some elliptic problems. Pacific Journal of Mathematics, 210(2), 215-228.
  • Dancer, E., Yan, S. (2003). Multi-layer solutions for an elliptic problem. Journal of Differential Equations, 194, 382-405. [More Information]
  • Dancer, E., Du, Y. (2003). On a free boundary problem arising from population biology. Indiana University Mathematics Journal, 52(1), 51-67.
  • Dancer, E., Yan, S. (2003). Peak solutions for an elliptic system of FitzHugh-Nagumo type. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, 11, 679-709.
  • Dancer, E. (2003). Real analyticity and non-degeneracy. Mathematische Annalen, 325(2), 369-392. [More Information]
  • Dancer, E. (2003). Some mountain-pass solutions for small diffusion. Differential and Integral Equations, 16(8), 1013-1024.
  • Dancer, E. (2003). Some near critical problems. Advances in Differential Equations, 8(5), 571-594.
  • Dancer, E., Du, Y. (2003). Some remarks on Liouville type results for quasilinear elliptic equations. Proceedings of the American Mathematical Society, 131(6), 1891-1899.
  • Dancer, E. (2002). Bifurcation from simple Eigenvalues and Eigenvalues of geometric multiplicity one. Bulletin of the London Mathematical Society, 34(5), 533-538. [More Information]
  • Campos, J., Dancer, E., Ortega, R. (2002). Dynamics in the neighbourhood of a continuum of fixed points. Annali di Matematica Pura ed Applicata, 180(4), 483-492. [More Information]
  • Dancer, E., Zhang, Z. (2002). Dynamics of Lotka-Volterra competition systems with large interaction. Journal of Differential Equations, 182(2), 470-489. [More Information]
  • Dancer, E., Du, Y. (2002). Effects of certain degeneracies in the predator-prey model. SIAM Journal On Mathematical Analysis, 34(2), 292-314.
  • Dancer, E., Yan, S. (2002). Multibump solutions for an elliptic problem in expanding domains. Communications in Partial Differential Equations, 27(1-2), 23-55. [More Information]
  • Dancer, E., Yan, S. (2002). On the profile of the changing sign mountain pass solutions for an elliptic problem. Transactions of the American Mathematical Society, 354(9), 3573-3600. [More Information]
  • Dancer, E. (2002). Some results for jumping nonlinearities. Topological Methods In Nonlinear Analysis, 19(2), 221-235.
  • Dancer, E., Huang, Q. (2002). Spatial independence of invariant sets of parabolic systems. Journal of Dynamics and Differential Equations, 14(2), 405-441.
  • Dancer, E. (2002). Uniqueness and generic non-degeneracy on strips. Advanced Nonlinear Studies, 2(2), 133-145.
  • Dancer, E. (2001). New solutions of equations on R^n. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, 30, 535-563.
  • Dancer, E., Campos, J. (2001). On the resonance set in a fourth-order equation with jumping nonlinearity. Differential and Integral Equations, 14, No. 3, 257-272.
  • Dancer, E., Aftalion, A. (2001). On the symmetry and uniqueness of solutions of the Ginzburg-Landau equations for small domains. Communications in Contemporary Mathematics, 3, No. 1, 1-14.
  • Dancer, E., Perera, K. (2001). Some remarks on the Fucik spectrum of the p-laplacian and critical groups. Journal of Mathematical Analysis and Applications, 254, 164-177.
  • Dancer, E., Yan, S., Lam,, K. (2001). The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrodinger equations. Abstract And Applied Analysis, 0.25138888889, 71-99.

2017

  • Dancer, E., Gladiali, F., Grossi, M. (2017). On the Hardy-Sobolev equation. Proceedings of the Royal Society of Edinburgh Section A (Mathematics), 147A, 299-336. [More Information]

2016

  • Ackermann, N., Dancer, E. (2016). Precise exponential decay for solutions of semilinear elliptic equations and its effect on the structure of the solution set for a real analytic nonlinearity. Differential and Integral Equations, 29(7-8), 757-774.

2015

  • Dancer, E., Daners, D., Hauer, D. (2015). A Liouville theorem for p-harmonic functions on exterior domains. Positivity, 19(3), 577-586. [More Information]
  • Daners, D., Hauer, D., Dancer, E. (2015). Uniform convergence of solutions to elliptic equations on domains with shrinking holes. Advances in Differential Equations, 20(5-6), 463-494.

2014

  • Dancer, E. (2014). A remark on stable solutions of nonlinear elliptic equations on R3 or R4. Differential and Integral Equations, 27(5-6), 483-488.
  • Dancer, E. (2014). On the converse problem for the gross-pitaevskii equations with a large parameter. Discrete and Continuous Dynamical Systems - Series A, 34(6), 2481-2493. [More Information]

2013

  • Dancer, E., Wang, K., Zhang, Z. (2013). Addendum to "The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture". Journal of Functional Analysis, 264(4), 1125-1129. [More Information]
  • Dancer, E. (2013). Addendum to: Stable and finite Morse index solutions for Dirichlet problems with small diffusion in a degenerate case and problems with infinite boundary values. Advanced Nonlinear Studies, 13(4), 791-794.
  • Dancer, E., Du, Y., Efendiev, M. (2013). Quasilinear Elliptic Equations on Half- and Quarter-spaces. Advanced Nonlinear Studies, 13(1), 115-136.
  • Dancer, E. (2013). Some bifurcation results for rapidly growing nonlinearities. Discrete and Continuous Dynamical Systems - Series S, 33(1), 153-161. [More Information]

2012

  • Dancer, E., Hillman, J., Pistoia, A. (2012). Deformation retracts to the fat diagonal and applications to the existence of peak solutions of nonlinear elliptic equations. Pacific Journal of Mathematics, 256(1), 67-78. [More Information]
  • Dancer, E., Wang, K., Zhang, Z. (2012). Dynamics of strongly competing systems with many species. Transactions of the American Mathematical Society, 364(2), 961-1005. [More Information]
  • Dancer, E., Weth, T. (2012). Liouville-type results for non-cooperative elliptic systems in a half-space. Journal of The London Mathematical Society, 86(1), 111-128. [More Information]
  • Dancer, E., Guo, Z., Wei, J. (2012). Non-radial singular solutions of Lane-Emden equations in $R^N$. Indiana University Mathematics Journal, 61(5), 1971-1996. [More Information]
  • Dancer, E. (2012). On domain perturbation for super-linear Neumann problems and a question of Y. Lou, W-M Ni and L. Su. Discrete and Continuous Dynamical Systems - Series A, 32(11), 3861-3869. [More Information]
  • Dancer, E., Wang, K., Zhang, Z. (2012). The limit equation for the Gross-Pitaevskii equations and S. Terracini's conjecture. Journal of Functional Analysis, 262(3), 1087-1131. [More Information]

2011

  • Dancer, E., Santra, S., Wei, J. (2011). Asymptotic behavior of the least energy solution of a problem with competing powers. Journal of Functional Analysis, 261, 2094-2134. [More Information]
  • Crooks, E., Dancer, E. (2011). Competition Systems With Strong Interaction on a Subdomain. Topological Methods In Nonlinear Analysis, 37(1), 37-53.
  • Dancer, E., Du, Y., Guo, Z. (2011). Finite Morse index solutions of an elliptic equation with supercritical exponent. Journal of Differential Equations, 250(8), 3281-3310. [More Information]
  • Dancer, E., Santra, S., Wei, J. (2011). Least energy nodal solution of a singular perturbed problem with jumping nonlinearity. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, X(1), 19-36.
  • Dancer, E. (2011). On the least point of the spectrum of certain cooperative linear systems with a large parameter. Journal of Differential Equations, 250(1), 33-38. [More Information]
  • Dancer, E., Wang, K., Zhang, Z. (2011). Uniform Holder estimate for singularly perturbed parabolic systems of Bose-Einstein condensates and competing species. Journal of Differential Equations, 251, 2737-2769. [More Information]

2010

  • Bartsch, T., Dancer, E., Wang, Z. (2010). A Liouville theorem, a-priori bounds, and bifurcating branches of positive solutions for a nonlinear elliptic system. Calculus of Variations and Partial Differential Equations, 37(3-4), 345-361. [More Information]
  • Dancer, E., Wei, J., Weth, T. (2010). A priori bounds versus multiple existence of positive solutions for a nonlinear Schrodinger system. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, AN 27(3), 953-969. [More Information]
  • Crooks, E., Dancer, E. (2010). Highly nonlinear large-competition limits of elliptic systems. Nonlinear Analysis, 73(5), 1447-1457. [More Information]
  • Dancer, E. (2010). New Results for Finite Morse Index Solutions on R^N and Applications. Advanced Nonlinear Studies, 10(3), 581-595. [More Information]
  • Dancer, E. (2010). Proofs of the Results in “Boundary-Value Problems for Weakly Nonlinear Ordinary Differential Equations�? Rendiconti dell' Istituto di matematica dell' Università di Trieste, 42(2010), 31-57.
  • Dancer, E., Santra, S. (2010). Singular perturbed problems in the zero mass case: asymptotic behavior of spikes. Annali di Matematica Pura ed Applicata, 189(2), 185-225. [More Information]

2009

  • Dancer, E. (2009). A Conley Index Calculation. Bulletin of the Australian Mathematical Society, 80(3), 510-520. [More Information]
  • Dancer, E., Micheletti, A., Pistoia, A. (2009). Multipeak solutions for some singularly perturbed nonlinear elliptic problems on Riemannian manifolds. Manuscripta Mathematica, 128(2), 163-193. [More Information]
  • Dancer, E., Farina, A. (2009). On the classification of solutions of -Delta u=e^u on R^N: stability outside a compact set and applications. Proceedings of the American Mathematical Society, 137(4), 1333-1338. [More Information]
  • Dancer, E. (2009). On the principal eigenvalue of linear cooperating elliptic systems with small diffusion. Journal of Evolution Equations, 9(3), 419-428. [More Information]
  • Dancer, E., Hilhorst, D., Yan, S. (2009). Peak solutions for the Dirichlet problem of an elliptic system. Discrete and Continuous Dynamical Systems - Series A, 24(3), 731-761. [More Information]
  • Dancer, E. (2009). Peak solutions without non-degeneracy conditions. Journal of Differential Equations, 246(8), 3077-3088. [More Information]
  • Bartsch, T., Dancer, E. (2009). Poincare-Hopf type formulas on convex sets of Banach spaces. Topological Methods In Nonlinear Analysis, 34(2), 213-229.
  • Dancer, E. (2009). Some remarks on half space problems. Discrete and Continuous Dynamical Systems - Series A, 25(1), 83-88. [More Information]
  • Dancer, E., Wei, J. (2009). Spike solutions in coupled nonlinear Schrodinger equations with attractive interaction. Transactions of the American Mathematical Society, 361(3), 1189-1208.
  • Dancer, E. (2009). Stable and finite Morse index solutions for Dirichlet problems with small diffusion in a degenerate case and problems with infinite boundary values. Advanced Nonlinear Studies, 9(4), 657-678.

2008

  • Dancer, E., Santra, S. (2008). Existence and multiplicity of solutions for a weakly coupled radial system in a ball. Communications on Pure and Applied Analysis, 7(4), 787-793. [More Information]
  • Dancer, E. (2008). Finite Morse index solutions of exponential problems. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 25(1), 173-179. [More Information]
  • Dancer, E. (2008). Finite Morse index solutions of supercritical problems. Journal fur die Reine und Angewandte Mathematik (Crelle's journal), 620(1), 213-233. [More Information]
  • Dancer, E. (2008). Moving plane methods for systems on half spaces. Mathematische Annalen, 342, 245-254. [More Information]
  • Dancer, E., Yan, S. (2008). On the Lazer-Mckenna conjecture involving critical and supercritical exponents. Methods and Applications of Analysis, 15(1), 97-120.
  • Dancer, E., Yan, S. (2008). The Lazer-McKenna conjecture and a free boundary problem in two dimensions. Journal of The London Mathematical Society, 78(3), 639-662. [More Information]

2007

  • Dancer, E., Yan, S. (2007). A new type of concentration solutions for a singularly perturbed elliptic problem. Transactions of the American Mathematical Society, 359(4), 1765-1790. [More Information]
  • Dancer, E. (2007). Conley indices on convex sets, attractor-repeller pairs and applications to multiple solutions of nonlinear elliptic equations. Journal of Fixed Point Theory and Applications, 1(1), 47-60. [More Information]
  • Dancer, E. (2007). Domain variation and non-uniqueness of homoclinic solutions of some partial differential equations on strips. Journal of Dynamics and Differential Equations, 19(3), 709-718. [More Information]
  • Crooks, E., Dancer, E., Hilhorst, D. (2007). Fast reaction limit and long time behavior for a competition-diffusion system with Dirichlet boundary conditions. Discrete and Continuous Dynamical Systems - Series B, 8(1), 39-44.
  • Dancer, E., Ren, X., Yan, S. (2007). On multiple radial solutions of a singularly perturbed nonlinear elliptic system. SIAM Journal On Mathematical Analysis, 38(6), 2005-2041. [More Information]
  • Dancer, E., Santra, S. (2007). On the superlinear Lazer-Mckenna conjecture: the non-homogeneous case. Advances in Differential Equations, 12(9), 961-993.
  • Dancer, E., Wei, J. (2007). Sign-changing solutions for supercritical elliptic problems in domains with small holes. Manuscripta Mathematica, 123(4), 493-511. [More Information]
  • Dancer, E. (2007). Supercritical finite Morse index solutions. Nonlinear Analysis, 66(1), 268-269. [More Information]

2006

  • Dancer, E., Du, Y. (2006). A uniqueness theorem for a free boundary problem. Proceedings of the American Mathematical Society, 134(11), 3223-3230. [More Information]
  • Dancer, E., Yan, S. (2006). Interior peak solutions for an elliptic system of FitzHugh-Nagumo type. Journal of Differential Equations, 229(2), 654-679. [More Information]
  • Dancer, E., Yan, S. (2006). Multipeak solutions for an elliptic system of Fitzhugh-Nagumo type. Mathematische Annalen, 335(3), 527-569. [More Information]
  • Bartsch, T., Dancer, E., Peng, S. (2006). On multi-bump semi-classical bound states of nonlinear Schrodinger equations with electromagnetic fields. Advances in Differential Equations, 11(7), 781-812.
  • Dancer, E. (2006). On stable and meta-stable solutions of the shadow system for the Geirer-Meinhardt equation. Advanced Nonlinear Studies, 6(3), 483-490. [More Information]
  • Dancer, E., Yan, S. (2006). Solutions with interior and boundary peaks for the Neumann problem of an elliptic system of FitzHugh-Nagumo type. Indiana University Mathematics Journal, 55(1), 217-258. [More Information]
  • Dancer, E. (2006). Stable and not too unstable solutions on Rn for small diffusion. In Brunner H, Zhao X-Q, Zou X, (Eds.), Nonlinear dynamics and evolution equations, (pp. 67-93). Providence, Rhode Island: American Mathematical Society.
  • Dancer, E., Shi, J. (2006). Uniqueness and nonexistence of positive solutions to semipositone problems. Bulletin of the London Mathematical Society, 38(6), 1033-1044. [More Information]
  • Dancer, E. (2006). Weak convergence, local bifurcations and uniqueness theorems. Accademia Nazionale dei Lincei. Atti. Matematica e Applicazioni. Rendiconti, 17(3), 243-255.

2005

  • Dancer, E., Geba, K., Rybicki, S. (2005). Classification of homotopy classes of equivariant gradient maps. Fundamenta Mathematicae, 185(1), 1-18.
  • Dancer, E., Yan, S. (2005). Multipeak solutions for the Neumann problem of an elliptic system of Fitzhugh-Nagumo type. Proceedings of the London Mathematical Society, 90(3), 209-244. [More Information]
  • Dancer, E., Yan, S. (2005). On the superlinear Lazer-McKenna conjecture. Journal of Differential Equations, 210(2), 317-351. [More Information]
  • Dancer, E., Yan, S. (2005). On the superlinear Lazer-McKenna conjecture: Part II. Communications in Partial Differential Equations, 30(9), 1331-1358. [More Information]
  • Dancer, E. (2005). Remarks on nonlinear elliptic problems on long domains. Advanced Nonlinear Studies, 5(2), 253-263.
  • Dancer, E. (2005). Some examples on solution structures for weakly nonlinear elliptic equations. Discrete and Continuous Dynamical Systems - Series A, 12(5), 817-826. [More Information]
  • Dancer, E. (2005). Stable and finite morse index solutions on Rn or on bounded domains with small diffusion. Transactions of the American Mathematical Society, 357(3), 1225-1243. [More Information]

2004

  • Dancer, E., Yan, S. (2004). A minimization problem associated with elliptic systems of FitzHugh-Nagumo type. Annales de l'Institut Henri Poincare (C) Analyse Non Lineaire, 21(2), 237-253. [More Information]
  • Dancer, E., Yan, S. (2004). Construction Of Various Types Of Solutions For An Elliptic Problem. Calculus of Variations and Partial Differential Equations, 20(1), 93-118. [More Information]
  • Dancer, E. (2004). Stable and finite morse index solutions on R^n or on bounded domains with small diffusion II. Indiana University Mathematics Journal, 53(1), 97-108.
  • Dancer, E. (2004). Stable Solutions On R\Sp N And The Primary Branch Of Some Non-Self-Adjoint Convex Problems. Differential and Integral Equations, 17(9-10), 961-970.

2003

  • Dancer, E., Du, Y., Ma, L. (2003). Asymptotic behavior of positive solutions of some elliptic problems. Pacific Journal of Mathematics, 210(2), 215-228.
  • Dancer, E., Yan, S. (2003). Multi-layer solutions for an elliptic problem. Journal of Differential Equations, 194, 382-405. [More Information]
  • Dancer, E., Du, Y. (2003). On a free boundary problem arising from population biology. Indiana University Mathematics Journal, 52(1), 51-67.
  • Dancer, E., Yan, S. (2003). Peak solutions for an elliptic system of FitzHugh-Nagumo type. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, 11, 679-709.
  • Dancer, E. (2003). Real analyticity and non-degeneracy. Mathematische Annalen, 325(2), 369-392. [More Information]
  • Dancer, E. (2003). Some mountain-pass solutions for small diffusion. Differential and Integral Equations, 16(8), 1013-1024.
  • Dancer, E. (2003). Some near critical problems. Advances in Differential Equations, 8(5), 571-594.
  • Dancer, E., Du, Y. (2003). Some remarks on Liouville type results for quasilinear elliptic equations. Proceedings of the American Mathematical Society, 131(6), 1891-1899.

2002

  • Dancer, E. (2002). Bifurcation from simple Eigenvalues and Eigenvalues of geometric multiplicity one. Bulletin of the London Mathematical Society, 34(5), 533-538. [More Information]
  • Campos, J., Dancer, E., Ortega, R. (2002). Dynamics in the neighbourhood of a continuum of fixed points. Annali di Matematica Pura ed Applicata, 180(4), 483-492. [More Information]
  • Dancer, E., Zhang, Z. (2002). Dynamics of Lotka-Volterra competition systems with large interaction. Journal of Differential Equations, 182(2), 470-489. [More Information]
  • Dancer, E., Du, Y. (2002). Effects of certain degeneracies in the predator-prey model. SIAM Journal On Mathematical Analysis, 34(2), 292-314.
  • Dancer, E., Yan, S. (2002). Multibump solutions for an elliptic problem in expanding domains. Communications in Partial Differential Equations, 27(1-2), 23-55. [More Information]
  • Dancer, E., Yan, S. (2002). On the profile of the changing sign mountain pass solutions for an elliptic problem. Transactions of the American Mathematical Society, 354(9), 3573-3600. [More Information]
  • Dancer, E. (2002). Some results for jumping nonlinearities. Topological Methods In Nonlinear Analysis, 19(2), 221-235.
  • Dancer, E., Huang, Q. (2002). Spatial independence of invariant sets of parabolic systems. Journal of Dynamics and Differential Equations, 14(2), 405-441.
  • Dancer, E. (2002). Uniqueness and generic non-degeneracy on strips. Advanced Nonlinear Studies, 2(2), 133-145.

2001

  • Dancer, E. (2001). New solutions of equations on R^n. Scuola Normale Superiore di Pisa. Annali. Classe di Scienze, 30, 535-563.
  • Dancer, E., Campos, J. (2001). On the resonance set in a fourth-order equation with jumping nonlinearity. Differential and Integral Equations, 14, No. 3, 257-272.
  • Dancer, E., Aftalion, A. (2001). On the symmetry and uniqueness of solutions of the Ginzburg-Landau equations for small domains. Communications in Contemporary Mathematics, 3, No. 1, 1-14.
  • Dancer, E., Perera, K. (2001). Some remarks on the Fucik spectrum of the p-laplacian and critical groups. Journal of Mathematical Analysis and Applications, 254, 164-177.
  • Dancer, E., Yan, S., Lam,, K. (2001). The effect of the graph topology on the existence of multipeak solutions for nonlinear Schrodinger equations. Abstract And Applied Analysis, 0.25138888889, 71-99.

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