摘要
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation -Δu=(integral ((|u(y)|^(2*)_μ/|x-y|~μ)dy) from Ω )|μ|^(2*_μ-2_u)+λu in Ω where Ω is a bounded dotain of R^N with Lipschitz boundary, λ is a real parameter, N≥3,2_μ~*=(2 N-μ)/(N-2)is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.
We establish some existence results for the Brezis-Nirenberg type problem of the nonlinear Choquard equation -Δu=（integral （（｜u（y）｜^（2＊）μ/｜x-y｜~μ）dy） from Ω ）｜μ｜^（2＊μ-2u）＋λu in Ω where Ω is a bounded dotain of R^N with Lipschitz boundary, λ is a real parameter, N≥3,2μ~＊=（2 N-μ）/（N-2）is the critical exponent in the sense of the Hardy-Littlewood-Sobolev inequality.
基金
supported by National Natural Science Foundation of China(Grant Nos.11571317 and 11671364)
Natural Science Foundation of Zhejiang(Grant No.LY15A010010)
