Existence of three solutions for a class of quasilinear elliptic systems involving the \((p(x),q(x))\)-Laplacian

DOI10.1016/j.na.2008.10.094zbMath1167.35359OpenAlexW2094484748MaRDI QIDQ1021752

Xiayang Shi, Jingjing Liu

Publication date: 9 June 2009

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.2008.10.094

zbMATH Keywords

Dirichlet problemthree solutions\((p(x),q(x))\)-LaplacianRicceri's three-critical-points theorem

Mathematics Subject Classification ID

Related Items (18)

Existence results for a Kirchhoff-type equations involving the fractional \(p_1(x)\) \& \(p_2(x)\)-Laplace operator ⋮ Multiplicity results for nonlinear Neumann boundary value problems involving \(p\)-Laplace type operators ⋮ Global existence, asymptotic stability and blow up of solutions for a nonlinear viscoelastic plate equation involving \((p(x), q(x))\)-Laplacian operator ⋮ On some degenerate quasilinear equations involving variable exponents ⋮ Multiple solutions for gradient elliptic systems with nonsmooth boundary conditions ⋮ Existence of three solutions for some equation of Kirchhoff type involving variable exponents ⋮ Multiplicity results for a differential inclusion problem with non-standard growth ⋮ Three solutions for a perturbed Navier problem ⋮ Existence and multiplicity of solutions for a class of quasilinear elliptic systems in Orlicz-Sobolev spaces ⋮ Existence of three solutions for a Navier boundary value problem involving the \((p(x),q(x))\)-biharmonic ⋮ Overview of differential equations with non-standard growth ⋮ Three solutions for equations involving nonhomogeneous operators of \(p\)-Laplace type in \(\mathbb R^N\) ⋮ Unnamed Item ⋮ Multiple solutions for elliptic \((p(x), q(x))\)-Kirchhoff-type potential systems in unbounded domains ⋮ Multiple solutions for a class of Neumann doubly eigenvalue boundary value systems involving the \((p_1(x),\dots,p_n(x))\)-Laplacian ⋮ Existence result for a gradient-type elliptic system involving a pair ofp(x) andq(x)-Laplacian operators ⋮ Existence of three solutions for a class of quasilinear elliptic systems involving the $p(x)$-Laplace operator ⋮ Three solutions for a class of quasilinear elliptic systems in Orlicz–Sobolev spaces

Cites Work

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• Remarks on Ricceri's variational principle and applications to the \(p(x)\)-Laplacian equations
• Multiple nonsemitrivial solutions for quasilinear elliptic systems
• Existence of three solutions for \(p(x)\)-Laplacian equations
• AVERAGING OF FUNCTIONALS OF THE CALCULUS OF VARIATIONS AND ELASTICITY THEORY
• EXISTENCE OF TWO NON-TRIVIAL SOLUTIONS FOR A CLASS OF QUASILINEAR ELLIPTIC VARIATIONAL SYSTEMS ON STRIP-LIKE DOMAINS
• 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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