Multiple positive solutions for a semilinear equation with critical exponent and prescribed singularity. (January 2016) - Chen, Yaoping; Chen, Jianqing
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.