Existence of three solutions for variable exponent elliptic systems

DOI10.1007/s11565-015-0225-8zbMath1332.35100OpenAlexW2093206682MaRDI QIDQ895818

Mostafa Allaoui

Publication date: 7 December 2015

Published in: Annali dell'Università di Ferrara. Sezione VII. Scienze Matematiche (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s11565-015-0225-8

zbMATH Keywords

variable exponent Sobolev spacecritical point theoremNavier value problem

Mathematics Subject Classification ID

Variational methods involving nonlinear operators (47J30) Weak solutions to PDEs (35D30) Critical points of functionals in context of PDEs (e.g., energy functionals) (35B38) Variational methods for higher-order elliptic equations (35J35) Quasilinear elliptic equations (35J62)

Cites Work

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• Infinitely many solutions for a perturbed nonlinear Navier boundary value problem involving the \(p\)-biharmonic
• On the spectrum of a fourth order elliptic equation with variable exponent
• Existence of solutions for \(p(x)\)-Laplacian equations with singular coefficients in \(\mathbb R^N\)
• Interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces
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• Existence and multiplicity of solutions for elliptic systems with nonstandard growth condition in \(\mathbb R^N\)
• Existence and asymptotic behavior of positive solutions for variable exponent elliptic systems
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• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• Existence of three solutions for a class of elliptic eigenvalue problems
• 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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