On problems driven by the \((p(\cdot),q(\cdot))\)-Laplace operator

DOI10.1007/S00009-019-1448-1zbMath1437.35225OpenAlexW2996219657MaRDI QIDQ2295496

Francesca Vetro, Calogero Vetro

Publication date: 13 February 2020

Published in: Mediterranean Journal of Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00009-019-1448-1

zbMATH Keywords

weak solutionscritical points\((p(\cdot), q(\cdot))\)-Laplace operator

Mathematics Subject Classification ID

Nonlinear elliptic equations (35J60) Variational methods for second-order elliptic equations (35J20)

Related Items (16)

Explicit criteria for the qualitative properties of differential equations with \(p\)-Laplacian-like operator ⋮ Mountain pass solution for the weighted Dirichlet \((p(z),q(z))\)-problem ⋮ Double phase obstacle problems with variable exponent ⋮ Existence and concentration of nodal solutions for a subcritical \textit{p\&q} equation ⋮ Three solutions to mixed boundary value problem driven by p(z)‐Laplace operator ⋮ Positive solutions for resonant (p,q)-equations with convection ⋮ Some new oscillation results for fourth-order neutral differential equations with a canonical operator ⋮ Anisotropic double-phase problems with indefinite potential: multiplicity of solutions ⋮ Higher order spectrum and quasi-linear boundary problems of discrete p-Laplacian ⋮ Existence and multiplicity of solutions for a class of anisotropic double phase problems ⋮ Convergence analysis for double phase obstacle problems with multivalued convection term ⋮ Positive solutions for parametric \((p(z),q(z))\)-equations ⋮ Double phase obstacle problems with multivalued convection and mixed boundary value conditions ⋮ Nonlinear singular problems with indefinite potential and a superlinear perturbation ⋮ Weak solutions for a (p(z),q(z))-Laplacian Dirichlet problem ⋮ Nonlinear equations of fourth-order with 𝑝-Laplacian like operators: Oscillation, methods and applications

Cites Work

• On superlinear \(p(x)\)-Laplacian problems without Ambrosetti and Rabinowitz condition
• On the superlinear problems involving \(p(x)\)-Laplacian-like operators without AR-condition
• Existence and multiplicity of weak solutions for elliptic Dirichlet problems with variable exponent
• Lebesgue and Sobolev spaces with variable exponents
• Anisotropic nonlinear Neumann problems
• Existence of solutions for \(p(x)\)-Laplacian Dirichlet problem.
• Topological and Variational Methods with Applications to Nonlinear Boundary Value Problems
• Relations between the mountain pass theorem and local minima
• Weak solutions to Dirichlet boundary value problem driven by p(x)-Laplacian-like operator
• Superlinear (p(z), q(z))-equations
• On the structure of the critical set of non-differentiable functions with a weak compactness condition
• On the spaces \(L^{p(x)}(\Omega)\) and \(W^{m,p(x)}(\Omega)\)

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