The existence of two nontrivial solutions via homological local linking for the non-coercive \(p\)-Laplacian Neumann problem

DOI10.1016/j.na.2008.10.021zbMath1387.35250OpenAlexW2003184777MaRDI QIDQ1015145

Donal O'Regan, Nikolaos S. Papageorgiou

Publication date: 7 May 2009

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2008.10.021

zbMATH Keywords

critical groups\(p\)-LaplacianPS-conditionC-conditionnoncoercive Euler functional

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) 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)

Cites Work

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• Existence and multiplicity of solutions for Neumann problems
• Critical point theory and Hamiltonian systems
• Three solutions to a Neumann problem for elliptic equations involving the \(p\)-Laplacian
• On a three critical points theorem
• Multiplicity results for a Neumann problem involving the \(p\)-Laplacian.
• Existence of infinitely many weak solutions for a Neumann problem
• On existence and multiplicity of solutions of Neumann boundary value problems for quasi-linear elliptic equations
• INFINITELY MANY SOLUTIONS OF THE NEUMANN PROBLEM FOR ELLIPTIC EQUATIONS INVOLVING THE p-LAPLACIAN
• Multiplicity Results for Nonlinear Neumann Problems
• Homological local linking
• Remarks on multiple nontrivial solutions for quasi-linear resonant problems
• Periodic solutions for second order systems with not uniformly coercive potential

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