Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík type resonance at infinity

DOI10.1016/J.NA.2008.02.117zbMath1170.35426OpenAlexW4232612976MaRDI QIDQ1004613

Mieko Tanaka

Publication date: 11 March 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.2008.02.117

zbMATH Keywords

mountain pass theorem\(p\)-LaplacianFučík spectrum

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) General topics in linear spectral theory for PDEs (35P05) 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 (4)

Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík type resonance at infinity. II ⋮ Existence of solutions for quasilinear elliptic equations with jumping nonlinearities under the Neumann boundary condition ⋮ Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík-type resonance at infinity. III ⋮ Elliptic hemivariational inequalities with nonhomogeneous Neumann boundary conditions and their applications to static frictional contact problems

Cites Work

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• Multiple nontrivial solutions for \(p\)-Laplacian equations with an asymmetric nonlinearity.
• Constant-sign and sign-changing solutions of a nonlinear eigenvalue problem involving the \(p\)-Laplacian.
• Critical groups and multiple solutions of the \(p\)-Laplacian equations
• Existence and multiplicity results for Dirichlet problems with \(p\)-Laplacian.
• Infinite dimensional Morse theory and multiple solution problems
• On the Fučík spectrum of the \(p\)-Laplacian
• Minimax theorems
• The beginning of the Fučik spectrum for the \(p\)-Laplacian
• Resonance problems for the \(p\)-Laplacian
• A strong maximum principle for some quasilinear elliptic equations
• C1 + α local regularity of weak solutions of degenerate elliptic equations
• Nodal and Multiple Constant Sign Solution for Equations with the p-Laplacian
• Abstract critical point theorems and applications to some nonlinear problems with “strong” resonance at infinity
• Boundary value problems with jumping nonlinearities
• On the Dirichlet problem for weakly non-linear elliptic partial differential equations
• SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS
• Multiple nontrivial solutions for nonlinear eigenvalue problems
• On harnack type inequalities and their application to quasilinear elliptic equations
• SOLUTIONS OF p-SUBLINEAR p-LAPLACIAN EQUATION VIA MORSE THEORY
• Some remarks on the Fučík spectrum of the \(p\)-Laplacian and critical groups
• Remarks on multiple nontrivial solutions for quasi-linear resonant problems

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