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

2019/09/14 by Sabri Bahrouni, Bahrouni, Sabri, Hichem Ounaies +1 · 4 citations
Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Differential Equations and Boundary Problems #FOS: Mathematics #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1909.06584

openalex publication_date 2019/09/14 · openalex created_date 2022/07/28 · openalex updated_date 2026/07/28

Abstract

In the present paper, we deal with a new continuous and compact embedding\ntheorems for the fractional Orlicz-Sobolev spaces, also, we study the existence\nof infinitely many nontrivial solutions for a class of non-local fractional\nOrlicz-Sobolev Schr "odinger equations whose simplest prototype is\n(-
triangle)^s_mu+V(x)m(u)=f(x,u),
x
in
mathbbR^d, where 0<s<1,\nd\≥2 and (- triangle)^s_m is the fractional M-Laplace operator. The\nproof is based on the variant Fountain theorem established by Zou.\n

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• On the singular elliptic problem involving the variable order fractional Musielak g_x,y-Laplacian
• Superlinear fractional Φ-Laplacian type problems via the nonlinear Rayleigh quotient with two parameters
• Comparison principle for Singular Fractional g- Laplacian Problems
• Fractional Orlicz-Sobolev embeddings into Campanato type spaces

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• Infinitely many solutions for a class of fractional Orlicz-Sobolev Schrödinger equations
• Introduction to fractional Orlicz-Sobolev spaces
• Basic results of fractional Orlicz-Sobolev space and applications to non-local problems
• Compact embedding theorems and a Lions' type Lemma for fractional\n Orlicz-Sobolev spaces
• Ground state solutions for a non-local type problem in fractional Orlicz Sobolev spaces