The critical Lazer-McKenna conjecture in low dimensions

DOI10.1016/j.jde.2008.05.002zbMath1155.35030OpenAlexW2083372588WikidataQ123134343 ScholiaQ123134343MaRDI QIDQ949633

Olivier Druet

Publication date: 21 October 2008

Published in: Journal of Differential Equations (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jde.2008.05.002

zbMATH Keywords

low dimensionsHopf's maximum principleLazer-McKenna conjecture

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) Critical exponents in context of PDEs (35B33) Nonlinear elliptic equations (35J60) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Variational methods for second-order elliptic equations (35J20)

Related Items (6)

Boundary bubbling solutions for a planar elliptic problem with exponential Neumann data ⋮ Bubbling solutions for an anisotropic planar elliptic problem with exponential nonlinearity ⋮ Elliptic equations with jumping nonlinearities involving high eigenvalues ⋮ The Lazer-McKenna conjecture for an anisotropic planar elliptic problem with exponential Neumann data ⋮ Multiple solutions for a class of elliptic equations with jumping nonlinearities ⋮ Existence and multiplicity of solutions for elliptic equations with jumping nonlinearities

Cites Work

• Pohozaev type obstructions and solutions of bounded energy for quasilinear elliptic equations with critical Sobolev growth. The conformally flat case
• The two-dimensional Lazer-McKenna conjecture for an exponential nonlinearity
• The Lazer-McKenna conjecture for an elliptic problem with critical growth
• Lazer-McKenna conjecture: the critical case
• On the number of solutions of a nonlinear Dirichlet problem
• Multiple solutions for a semilinear boundary value problem: a computational multiplicity proof.
• On the superlinear Lazer-McKenna conjecture
• The Lazer-McKenna conjecture for an elliptic problem with critical growth. II
• On a conjecture related to the number of solutions of a nonlinear Dirichlet problem
• Asymptotic symmetry and local behavior of semilinear elliptic equations with critical sobolev growth
• Concentration estimates for Emden-Fowler equations with boundary singularities and critical growth
• On the Superlinear Lazer–McKenna Conjecture: Part II
• Unnamed Item

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