Existence result for variable exponents elliptic system with lack of compactness

DOI10.1080/00036811.2020.1800652zbMath1490.35147OpenAlexW3046611414MaRDI QIDQ5072936

O. Saifia, Jean Velin

Publication date: 5 May 2022

Published in: Applicable Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1080/00036811.2020.1800652

zbMATH Keywords

Dirichlet problemconcentration-compactness principle\((p(x),q(x))\)-Laplacian

Mathematics Subject Classification ID

Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations with (p)-Laplacian (35J92) Boundary value problems for second-order elliptic systems (35J57)

Cites Work

• On the Sobolev embedding theorem for variable exponent spaces in the critical range
• Harnack inequality for hypoelliptic ultraparabolic equations with a singular lower order term
• Existence results for some nonlinear elliptic system with lack of compactness
• Existence and multiplicity of solutions for \(p(x)\)-Laplacian equations in \(\mathbb R^N\)
• Existence and nonexistence of ground state solutions to singular elliptic systems
• A fourth order singular elliptic problem involving \(p\)-biharmonic operator
• Solutions for \(p(x)\)-Laplacian Dirichlet problems with singular coefficients
• A Relation Between Pointwise Convergence of Functions and Convergence of Functionals
• The concentration-compactness principle for variable exponent spaces and applications
• Compact embeddings for Sobolev spaces of variable exponents and existence of solutions for nonlinear elliptic problems involving the p(x)-Laplacian and its critical exponent
• Almost everywhere convergence of the gradients of solutions to elliptic and parabolic equations
• An Integral Inequality
• Twoweak solutions for a singular (p,q)-Laplacian problem
• Compact imbedding theorems with symmetry of Strauss-Lions type for the space \(W^{1,p(x)}(\Omega)\)
• Sobolev embedding theorems for spaces \(W^{k,p(x)}(\Omega)\)
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
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