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

DOI10.1016/j.na.2009.01.186zbMath1177.35099OpenAlexW2004185315MaRDI QIDQ923961

Mieko Tanaka

Publication date: 24 July 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.2009.01.186

zbMATH Keywords

mountain pass theoremFučík spectrum of the \(p\)-Laplacian

Mathematics Subject Classification ID

Nonlinear boundary value problems for linear elliptic equations (35J65) General topics in linear spectral theory for PDEs (35P05) 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 (5)

Sign-changing and constant-sign solutions for \(p\)-Laplacian problems with jumping nonlinearities ⋮ On the antimaximum principle for the \(p\)-Laplacian and its sublinear perturbations ⋮ 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 ⋮ MHD micropolar fluid flow with thermal radiation and thermal diffusion in a rotating frame

Cites Work

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• Existence and multiplicity results for Dirichlet problems with \(p\)-Laplacian.
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• Resonance problems for 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
• EXISTENCE OF SOLUTIONS FOR ASYMPTOTICALLY ‘LINEAR’ ${p}$-LAPLACIAN EQUATIONS
• THE EXISTENCE OF MULTIPLE SOLUTIONS 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
• Nonlinear boundary value problems with concave nonlinearities near the origin
• Remarks on multiple nontrivial solutions for quasi-linear resonant problems

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