On the Brezis-Nirenberg type critical problem for nonlinear Choquard equation

2016/04/04 by Gao, Fashun, Yang, Minbo · 11 citations
#35J25 #35J65 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.1604.00826

Abstract

We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation -Δu =(∫_Ω\frac|u|^2_μ^∗|x-y|^μdy)|u|^2_μ^∗-2u+λu\4.14mmin\1.14mm Ω, where Ω is a bounded domain of ℝ^N, with Lipschitz boundary, λ is a real parameter, N≥3, 2_μ^∗=(2N-μ)/(N-2) is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.

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