Multiple positive solutions for a semilinear equation with critical exponent and prescribed singularity. (January 2016)

• Record Type: Journal Article
• Authors: Chen, Yaoping; Chen, Jianqing
• Is Part Of: Nonlinear analysis. Volume 130(2015)
• Page Start: 121
• Page End: 137
• Publication Date: 2016-01
• Subjects: 35J20 -- 35J60; Singular potential -- Critical Sobolev exponent -- Variational methods -- Multiple positive solutions; Mathematical analysis -- Periodicals; Functional analysis -- Periodicals; Nonlinear theories -- Periodicals; Analyse mathématique -- Périodiques; Analyse fonctionnelle -- Périodiques; Théories non linéaires -- Périodiques; Functional analysis; Mathematical analysis; Nonlinear theories; Periodicals; Electronic journals; 515.7248
• DOI: 10.1016/j.na.2015.10.007
• Languages: English
• ISSNs: 0362-546X

Abstract

Abstract: This paper is devoted to the study of a semilinear equation of the form: − Δ u − μ V ( x ) u = | u | 2 ∗ − 2 u + θ h ( x ), u ∈ H 0 1 ( Ω ), where Ω ⊂ R N ( N ≥ 3 ) is an open bounded domain with smooth boundary ∂ Ω, 0 < μ < μ ̄ = ( N − 2 2 ) 2, 2 ∗ = 2 N N − 2, h ( x ) > 0 and V ( x ) has prescribed finitely many singular points. Using variational methods, we establish some existence and multiplicity of positive solutions for the problem.