Multiplicity results for nonlocal critical problems involving Hardy potential in the whole space

被引：1

作者：

Abdellaoui, B. ^{[1
]}

Attar, A. ^{[1
]}

Boukarabila, Y. O. ^{[1
]}

Laamri, E-H ^{[2
]}

机构：

[1] Univ Abou Bakr Belkaid, Dept Math, Lab Anal Nonlineaire & Math Appl, Tilimsen, Algeria

[2] Univ Lorraine, Inst Elie Cartan Lorraine, Vanduvre Les Nancy, France

来源：

COMPLEX VARIABLES AND ELLIPTIC EQUATIONS | 2023年 / 68卷 / 03期

关键词：

Fractional Laplacian; Hardy's inequality; the concentration-compactness arguments; Palais-Smale conditions; multiplicity of solutions; CONCENTRATION-COMPACTNESS PRINCIPLE; INEQUALITIES; EQUATIONS; CALCULUS;

D O I：

10.1080/17476933.2021.1998016

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

The aim of this paper is to study a nonlocal elliptic problem in R-N (denoted as (P-lambda) below) involving the fractional Laplacian, a linear Hardy potential term and a critical nonlinear term. According to suitable assumptions on the set of extremal points of the functional coefficients, we prove that (P-lambda) has multiple positive solutions, and we determine their precise behavior near the extremal points. This work extends a previous article by the first author et al. on the local case.

引用

页码：461 / 497

页数：37

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