Embedding theorems in the fractional Orlicz-Sobolev space and applications to non-local problems

DOI10.3934/dcds.2020155zbMath1436.35090arXiv1909.06584OpenAlexW3010015787MaRDI QIDQ2306874

Sabri Bahrouni, Hichem Ounaies

Publication date: 26 March 2020

Published in: Discrete and Continuous Dynamical Systems (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1909.06584

zbMATH Keywords

Schrödinger operatorfractional \(p\)-Laplaciancompact embedding theoremfractional Orlicz-Sobolev space

Mathematics Subject Classification ID

Spaces of measurable functions ((L^p)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.) (46E30) Schrödinger operator, Schrödinger equation (35J10) Fractional partial differential equations (35R11)

Related Items (22)

Least-energy nodal solutions of nonlinear equations with fractional Orlicz–Sobolev spaces ⋮ Problems involving the fractional g-Laplacian with lack of compactness ⋮ Fractional N-Laplacian boundary value problems with jumping nonlinearities in the fractional Orlicz-Sobolev spaces ⋮ Fractional Orlicz-Sobolev embeddings ⋮ Existence and multiplicity of solutions to magnetic Kirchhoff equations in Orlicz-Sobolev spaces ⋮ Sign-changing solution for a generalized Kirchhoff problem in the fractional Orlicz-Sobolev space with nonsmooth nonlinearity ⋮ Variational eigenvalues of the fractional g-Laplacian ⋮ Global Hölder regularity for eigenfunctions of the fractional \(g\)-Laplacian ⋮ A new class of fractional Orlicz-Sobolev space and singular elliptic problems ⋮ On the L^∞‐regularity for fractional Orlicz problems via Moser's iteration ⋮ Existence and multiplicity of solutions for a Dirichlet problem in fractional Orlicz-Sobolev spaces ⋮ On fractional Musielak-Sobolev spaces and applications to nonlocal problems ⋮ Infinitely many solutions for problems in fractional Orlicz-Sobolev spaces ⋮ On the limit as \(s\rightarrow 0^+\) of fractional Orlicz-Sobolev spaces ⋮ Maximum principles, Liouville theorem and symmetry results for the fractional \(g\)-Laplacian ⋮ Compact embedding theorems and a Lions' type lemma for fractional Orlicz-Sobolev spaces ⋮ On the limit as \(s\to 1^-\) of possibly non-separable fractional Orlicz-Sobolev spaces ⋮ Existence of a solution to a nonlocal Schrödinger system problem in fractional modular spaces ⋮ Hardy and Poincaré inequalities in fractional Orlicz-Sobolev spaces ⋮ Neumann and Robin type boundary conditions in Fractional Orlicz-Sobolev spaces ⋮ Regularity for nonlocal problems with non-standard growth ⋮ Ground state and nodal solutions for fractional Orlicz problems with lack of regularity and without the Ambrosetti-Rabinowitz condition

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