Multiple nontrivial solutions for nonlinear eigenvalue problems

DOI10.1090/S0002-9939-07-08927-7zbMath1189.35215OpenAlexW1987395148MaRDI QIDQ5308134

Motreanu, Dumitru, Nikolaos S. Papageorgiou, Viorica V. Motreanu

Publication date: 27 September 2007

Published in: Proceedings of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9939-07-08927-7

zbMATH Keywords

truncationnonlinear eigenvalue problem\(p\)-Laplacianstrong maximum principleupper-lower solutionprincipal and second eigenvaluesecond deformation Lemma

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Maximum principles in context of PDEs (35B50) Degenerate elliptic equations (35J70) Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (12)

Existence of multiple solutions with precise sign information for superlinear Neumann problems ⋮ Sign-changing solutions for nonlinear elliptic problems depending on parameters ⋮ Multiplicity of solutions on a nonlinear eigenvalue problem for \(p(x)\)-Laplacian-like operators ⋮ Bifurcation phenomena for nonlinear superdiffusive Neumann equations of logistic type ⋮ Nonlinear elliptic equations with an asymptotically linear reaction term ⋮ Multiple constant sign and nodal solutions for nonlinear elliptic equations with the \(p\)-Laplacian ⋮ Multiple positive solutions for nonlinear eigenvalue problems with the \(p\)-Laplacian ⋮ Multiple solutions for superlinear \(p\)-Laplacian Neumann problems ⋮ Constant-sign and sign-changing solutions for nonlinear eigenvalue problems ⋮ Existence of a non-trivial solution for the \(p\)-Laplacian equation with Fučík type resonance at infinity ⋮ Eigenvalue problems for hemivariational inequalities ⋮ Multiple solutions for nonlinear Neumann problems driven by a nonhomogeneous differential operator

Cites Work

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• A strong maximum principle for some quasilinear elliptic equations
• Boundary regularity for solutions of degenerate elliptic equations
• 3.—A Criterion for the Existence of Solutions of Non-linear Elliptic Boundary Value Problems
• Multiple solutions for a class of semilinear elliptic equations
• SOBOLEV VERSUS HÖLDER LOCAL MINIMIZERS AND GLOBAL MULTIPLICITY FOR SOME QUASILINEAR ELLIPTIC EQUATIONS

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