Renormalized solutions for the fractional \(p(x)\)-Laplacian equation with \(L^1\) data

DOI10.1016/j.na.2019.111610zbMath1433.35156arXiv1708.04481OpenAlexW2971292011MaRDI QIDQ2280392

Chao Zhang, Xia Zhang

Publication date: 18 December 2019

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

Full work available at URL: https://arxiv.org/abs/1708.04481

zbMATH Keywords

Dirichlet problemexistence and uniqueness resultsfractional \(p(x)\)-Laplacian

Mathematics Subject Classification ID

Boundary value problems for higher-order elliptic equations (35J40) Existence problems for PDEs: global existence, local existence, non-existence (35A01) Fractional partial differential equations (35R11) Quasilinear elliptic equations with (p)-Laplacian (35J92) Uniqueness problems for PDEs: global uniqueness, local uniqueness, non-uniqueness (35A02)

Related Items (19)

VARIATIONAL ANALYSIS FOR FRACTIONAL EQUATIONS WITH VARIABLE EXPONENTS: EXISTENCE, MULTIPLICITY AND NONEXISTENCE RESULTS ⋮ Multiplicity of solutions for a class of fractional \(p(x,\cdot)\)-Kirchhoff-type problems without the Ambrosetti-Rabinowitz condition ⋮ Existence results for a Kirchhoff-type equation involving fractional \(p(x)\)-Laplacian ⋮ Existence results for a Kirchhoff-type equations involving the fractional \(p_1(x)\) \& \(p_2(x)\)-Laplace operator ⋮ Infinitely many solutions for a doubly nonlocal fractional problem involving two critical nonlinearities ⋮ WEAK SOLUTION FOR NONLINEAR FRACTIONAL P(.)-LAPLACIAN PROBLEM WITH VARIABLE ORDER VIA ROTHE'S TIME-DISCRETIZATION METHOD ⋮ The topological degree methods for the fractional p(·)-Laplacian problems with discontinuous nonlinearities ⋮ Infinitely many solutions for a class of fractional Robin problems with variable exponents ⋮ On a class of fractional systems with nonstandard growth conditions ⋮ Local regularity for nonlocal equations with variable exponents ⋮ On a class of fractional p (⋅,⋅)−Laplacian problems with sub-supercritical nonlinearities ⋮ On the solutions of nonlocal 1-Laplacian equation with \(L^1\)-data ⋮ Solutions of the mean curvature equation with the Nehari manifold ⋮ Eigenvalue problems involving the fractional \(p(x)\)-Laplacian operator ⋮ Strauss and Lions type theorems for the fractional Sobolev spaces with variable exponent and applications to nonlocal Kirchhoff-Choquard problem ⋮ Robin fractional problems with symmetric variable growth ⋮ Negative energy solutions for a new fractional \(p(x)\)-Kirchhoff problem without the (AR) condition ⋮ Remarks on eigenvalue problems for fractional p ( · )-Laplacian ⋮ On the fractional elliptic problems with difference in the Orlicz-Sobolev spaces

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