BASIC RESULTS OF FRACTIONAL ORLICZ-SOBOLEV SPACE AND APPLICATIONS TO NON-LOCAL PROBLEMS

被引：48

作者：

Bahrouni, Sabri ^{[1
]}

Ounaies, Hichem ^{[1
]}

Tavares, Leandro S. ^{[2
]}

机构：

[1] Univ Monastir, Fac Sci, Math Dept, Monastir 5019, Tunisia

[2] Univ Fed Cariri, Ctr Ciencias & Tecnol, BR-63048080 Juazeiro Do Norte, CE, Brazil

来源：

TOPOLOGICAL METHODS IN NONLINEAR ANALYSIS | 2020年 / 55卷 / 02期

关键词：

Fractional Orlicz-Sobolev space; fractional M-Laplacian; nonlocal problems; existence of solution; DIFFERENTIAL-OPERATORS; POSITIVE SOLUTIONS; LAPLACIAN; EQUATIONS;

D O I：

10.12775/TMNA.2019.111

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we study the interplay between the Orlicz- Sobolev spaces L-M and W(1,M )and the fractional Sobolev spaces W-s,W- p. More precisely, we give some qualitative properties of a new fractional Orlicz-Sobolev space W-s,W-M, where s is an element of (0, 1) and M is a Young function. We also study a related non-local operator, which is a fractional version of the nonhomogeneous M-Laplace operator. As an application, we prove existence of a weak solution for a non-local problem involving the new fractional M-Laplacian operator.

引用

页码：681 / 695

页数：15

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