Eigenvalues for a class of singular problems involving \(p(x)\)-biharmonic operator and \(q(x)\)-Hardy potential

DOI10.1515/anona-2020-0042zbMath1429.35166OpenAlexW2983982511MaRDI QIDQ2281673

Abdelouahed El Khalil, Mohamed Laghzal, My Driss Morchid Alaoui, Abdelfattah Touzani

Publication date: 3 January 2020

Published in: Advances in Nonlinear Analysis (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/anona-2020-0042

zbMATH Keywords

variational methodsnonlinear eigenvalue problemsHardy-Rellich inequality\(p(x)\)-biharmonic operatorLjusternik-Schnirelman

Mathematics Subject Classification ID

Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs (35P30) Boundary value problems for higher-order elliptic equations (35J40) Abstract critical point theory (Morse theory, Lyusternik-Shnirel'man theory, etc.) in infinite-dimensional spaces (58E05) Nonlinear spectral theory, nonlinear eigenvalue problems (47J10) Variational methods for higher-order elliptic equations (35J35) Quasilinear elliptic equations (35J62) Singular elliptic equations (35J75)

Related Items (5)

On a singular Kirchhoff type problems driven by p(⋅)-Laplacian operator ⋮ On a \(p(x)\)-biharmonic Kirchhoff type problem with indefinite weight and no flux boundary condition ⋮ Unnamed Item ⋮ Mixed finite element method for a beam equation with the \(p(x)\)-biharmonic operator ⋮ Low perturbations of p-biharmonic equations with competing nonlinearities

Cites Work

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• Lebesgue and Sobolev spaces with variable exponents
• Multiplicity of solutions for \(p(x)\)-polyharmonic elliptic Kirchhoff equations
• On the spectrum of a fourth order elliptic equation with variable exponent
• Interpolation inequalities for derivatives in variable exponent Lebesgue-Sobolev spaces
• Overview of differential equations with non-standard growth
• Ljusternik-Schnirelmann theory on \(C^ 1\)-manifolds
• Explicit constants for Rellich inequalities in \(L_p(\Omega)\)
• A Knobloch-type result for \(p(t\))-Laplacian systems.
• A simple approach to Hardy inequalities
• Nonlinear elliptic equations with variable exponent: old and new
• Solutions for Neumann boundary value problems involving \(p(x)\)-Laplace operators
• On the spectrum of the p-biharmonic operator involving p-Hardy's inequality
• The Hardy–Rellich inequality for polyharmonic operators
• Über konjugierte Exponentenfolgen
• Partial Differential Equations with Variable Exponents
• Existence and multiplicity of solutions for a Neumann problem involving the \(p(x)\)-Laplace operator
• A multiplicity result for a nonlinear degenerate problem arising in the theory of electrorheological fluids
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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