Remarks on the existence of three solutions for the \(p(x)\)-Laplacian equations

DOI10.1016/j.na.2010.12.013zbMath1210.35132OpenAlexW2078806751MaRDI QIDQ531686

Chao Ji

Publication date: 19 April 2011

Published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.na.2010.12.013

zbMATH Keywords

Dirichlet problemNeumann problemvariable exponent spaces\(p(x)\)-Laplacianthree solutions

Mathematics Subject Classification ID

Boundary value problems for second-order elliptic equations (35J25) Degenerate elliptic equations (35J70) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Quasilinear elliptic equations with (p)-Laplacian (35J92)

Related Items (17)

On a \(p(x)\)-biharmonic problem with Navier boundary condition ⋮ Three solutions for a partial discrete Dirichlet boundary value problem with \(p\)-Laplacian ⋮ Multiplicity results for elliptic problems with variable exponent and nonhomogeneous Neumann conditions ⋮ Critical points approaches to elliptic problems driven by a \(p(x)\)-Laplacian ⋮ Existence and multiplicity results for nonlinear problems involving the p(x)-Laplace operator ⋮ On the Steklov problem involving the p(x)-Laplacian with indefinite weight ⋮ A note on nonlinear fourth-order elliptic equations on \(\mathbb R ^N\) ⋮ On a class of non-local discrete boundary value problepm ⋮ Existence results for a Neumann problem involving the \(p(x)\)-Laplacian with discontinuous nonlinearities ⋮ Existence and multiplicity of solutions for anisotropic elliptic equation ⋮ Existence and nonexistence of solutions for p(x)-curl systems arising in electromagnetism ⋮ Unnamed Item ⋮ Existence of solutions for an anisotropic elliptic problem with variable exponent and singularity ⋮ Multiple solutions for a class of Neumann doubly eigenvalue boundary value systems involving the \((p_1(x),\dots,p_n(x))\)-Laplacian ⋮ Existence of solutions for nonlocal elliptic systems involving \(p(x)\)-Laplace operator ⋮ Unnamed Item ⋮ Multi-bump solutions for quasilinear elliptic equations with variable exponents and critical growth in ℝN

Cites Work

• Perturbation for a \(p(x)\)-Laplacian equation involving oscillating nonlinearities in \(R^N\)
• A further three critical points theorem
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Existence of infinitely many solutions for a Neumann problem involving the \(p(x)\)-Laplacian
• Existence of three solutions for \(p(x)\)-Laplacian equations
• A note on the Neumann problem
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)
• Unnamed Item
• Unnamed Item

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