Multiple solutions for the \(p(x)\)-Laplacian problem involving critical growth with a parameter

DOI10.1186/1687-2770-2013-223zbMath1297.35091OpenAlexW2105360060WikidataQ59302019 ScholiaQ59302019MaRDI QIDQ2252584

Xudong Shang, Yingchen Yang, Ji Hui Zhang

Publication date: 18 July 2014

Published in: Boundary Value Problems (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1186/1687-2770-2013-223

zbMATH Keywords

critical Sobolev exponentsconcentration-compactness principle\(p(x)\)-Laplacian problem

Mathematics Subject Classification ID

Variational methods for second-order elliptic equations (35J20) Quasilinear elliptic equations (35J62) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Cites Work

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Existence and multiplicity of solutions for a \(p(x)\)-Laplacian equation with critical growth
• Infinitely many solutions for elliptic problems with variable exponent and nonlinear boundary conditions
• On the Sobolev trace theorem for variable exponent spaces in the critical range
• On the asymptotic behavior of variable exponent power-law functionals and applications
• Infinitely many positive solutions for a \(p(x)\)-Kirchhoff-type equation
• Positive periodic solutions for a system of anisotropic parabolic equations
• \(\Gamma \)-convergence of power-law functionals with variable exponents
• The principle of concentration compactness in \(L^{p(x)}\) spaces and its application
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Multiplicity of solutions for quasilinear elliptic problems involving critical Sobolev exponents
• Dual variational methods in critical point theory and applications
• Existence and multiplicity results for elliptic problems with \(p(\cdot)\)-growth conditions
• Existence of solutions for \(p(x)\)-Laplacian problems on a bounded domain
• The concentration-compactness principle for variable exponent spaces and applications
• Multiple solutions for a class of p ( x )-Laplacian equations in involving the critical exponent
• On a class of nonlinear problems involving a p(x)-Laplace type operator
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Variable Exponent, Linear Growth Functionals in Image Restoration
• Introduction to the Theory of Bases
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)