Existence and multiplicity of solutions to a nonlocal elliptic PDE with variable exponent and nonlinear boundary conditions

DOI10.21494/ISTE.OP.2022.0885zbMath1522.35222MaRDI QIDQ6177219

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Publication date: 31 August 2023

Published in: Advances in Pure and Applied Mathematics (Search for Journal in Brave)

zbMATH Keywords

existencenonlinear boundary conditionsNehari manifold\(p(x)\)-Laplacian elliptic system

Mathematics Subject Classification ID

Variational methods applied to PDEs (35A15) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations with (p)-Laplacian (35J92) Nonlinear boundary value problems for nonlinear elliptic equations (35J66) Boundary value problems for second-order elliptic systems (35J57)

Cites Work

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• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
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• Regularity results for a class of functionals with non-standard growth
• 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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