Multiplicity results for nonlocal critical problems involving Hardy potential in the whole space. Issue 3 (4th March 2023)

• Record Type: Journal Article
• Authors: Abdellaoui, B.; Attar, A.; Boukarabila, Y. O.; Laamri, E. -H.
• Is Part Of: Complex variables and elliptic equations. Volume 68:Issue 3(2023)
• Page Start: 461
• Page End: 497
• Publication Date: 2023-03-04
• Subjects: Fractional Laplacian -- Hardy's inequality -- the concentration-compactness arguments -- Palais–Smale conditions -- multiplicity of solutions; 35B25 -- 35B65 -- 35J58 -- 35R09 -- 47G20; Functions of complex variables -- Periodicals; Differential equations, Elliptic -- Periodicals; 515.905
• DOI: 10.1080/17476933.2021.1998016
• Languages: English
• ISSNs: 1747-6933

Abstract

Abstract : The aim of this paper is to study a nonlocal elliptic problem in R N (denoted as ( P λ ) 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 λ ) 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.