General fractional Sobolev space with variable exponent and applications to nonlocal problems

DOI10.1007/s43036-020-00062-wzbMath1461.46026arXiv1901.05687OpenAlexW3016569180MaRDI QIDQ2193468

Elhoussine Azroul, Mohammed Shimi, Abdelmoujib Benkirane

Publication date: 18 August 2020

Published in: Advances in Operator Theory (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1901.05687

zbMATH Keywords

mountain pass theoremMinty-Browder theorem\(p(x, . )\)-Kirchhoff-type problems

Mathematics Subject Classification ID

Integro-ordinary differential equations (45J05) Sobolev spaces and other spaces of ``smooth functions, embedding theorems, trace theorems (46E35) Integro-differential operators (47G20) Fractional partial differential equations (35R11)

Related Items (10)

Notes on aplications of the dual fountain theorem to local and nonlocal elliptic equations with variable exponent ⋮ Existence results for a Kirchhoff-type equations involving the fractional \(p_1(x)\) \& \(p_2(x)\)-Laplace operator ⋮ On a class of nonlocal problems in new fractional Musielak-Sobolev spaces ⋮ Embedding and extension results in fractional Musielak–Sobolev spaces ⋮ Bourgain, Brezis and Mironescu theorem for fractional Sobolev spaces with variable exponents ⋮ Local regularity for nonlocal equations with variable exponents ⋮ Existence and multiplicity of solutions for fractional \(p(x)\)-Kirchhoff-type problems ⋮ Infinitely many solutions for Schrödinger-Kirchhoff-type equations involving the fractional \(p(x, \cdot )\)-Laplacian ⋮ Strauss and Lions type theorems for the fractional Sobolev spaces with variable exponent and applications to nonlocal Kirchhoff-Choquard problem ⋮ Eigenvalue problem associated with nonhomogeneous integro-differential operators

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