On an open problem involving the \(p(x)\)-Laplacian-A further study on the multiplicity of weak solutions to \(p(x)\)-Laplacian equations

DOI10.1016/j.na.2007.06.044zbMath1144.35390OpenAlexW2026803045MaRDI QIDQ943695

Jinghua Yao, Xiao-Yan Wang

Publication date: 10 September 2008

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.2007.06.044

zbMATH Keywords

weak solutioncritical point\(p(x)\)-Laplacianvariable exponent Sobolev spacesymmetric mountain pass Lemma

Mathematics Subject Classification ID

Degenerate elliptic equations (35J70) Variational methods for second-order elliptic equations (35J20)

Related Items

Existence and blow-up rate of large solutions of \(p(x)\)-Laplacian equations with gradient terms ⋮ Existence results for Schrödinger \(p(\cdot)\)-Laplace equations involving critical growth in \(\mathbb{R}^N$ ⋮ Modular uniform convexity structures and applications to boundary value problems with non-standard growth ⋮ Multiple solutions of double phase variational problems with variable exponent ⋮ Multiple solutions with constant sign of a Dirichlet problem for a class of elliptic systems with variable exponent growth ⋮ Compact Sobolev embedding theorems involving symmetry and its application ⋮ Overview of differential equations with non-standard growth ⋮ Positive solutions for a class of \(p(x)\)-Laplacian equation involving concave-convex nonlinearities ⋮ INFINITELY MANY LOW- AND HIGH-ENERGY SOLUTIONS FOR A CLASS OF ELLIPTIC EQUATIONS WITH VARIABLE EXPONENT ⋮ Infinitely many small solutions to an elliptic PDE of variable exponent with a singular nonlinearity

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