Existence of solutions and positivity of the infimum eigenvalue for degenerate elliptic equations with variable exponents

Publication date: 21 January 2015

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: http://aimsciences.org/journals/displayPaperPro.jsp?paperID=9252

zbMATH Keywords

eigenvalue mountain pass theorem fountain theorem $p(x)$-Laplacian weighted variable exponent Lebesgue-Sobolev spaces

Mathematics Subject Classification ID

General topics in linear spectral theory for PDEs (35P05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Nonlinear elliptic equations (35J60) Degenerate elliptic equations (35J70) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Variational methods for second-order elliptic equations (35J20)

Related Items (13)

Existence results for degenerate $p(x)$-Laplace equations with Leray-Lions type operators ⋮ A-priori bounds and existence for solutions of weighted elliptic equations with a convection term ⋮ Existence results for Schrödinger $p(\cdot)$-Laplace equations involving critical growth in $\mathbb{R}^N$ ⋮ On sufficient ``local conditions for existence results to generalized \(p(.)$-Laplace equations involving critical growth ⋮ Positivity of the infimum eigenvalue for the $p(x)$-triharmonic operator with variable exponents ⋮ Existence and some properties of solutions for degenerate elliptic equations with exponent variable ⋮ Existence of an unbounded branch of the set of solutions for equations of $p(x)$-Laplace type ⋮ Existence and multiplicity of solutions for Kirchhoff-Schrödinger type equations involving $p(x)$-Laplacian on the entire space $\mathbb{R}^N$ ⋮ EXISTENCE OF A POSITIVE INFIMUM EIGENVALUE FOR THE p(x)-LAPLACIAN NEUMANN PROBLEMS WITH WEIGHTED FUNCTIONS ⋮ Unnamed Item ⋮ Schrödinger p⋅–Laplace equations in RN involving indefinite weights and critical growth ⋮ Mountain pass type solutions and positivity of the infimum eigenvalue for quasilinear elliptic equations with variable exponents ⋮ Existence of nontrivial solutions for equations of $p(x)$-Laplace type without Ambrosetti and Rabinowitz condition

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