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 dota...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.展开更多
基金supported by National Natural Science Foundation of China(Grant Nos.11571317 and 11671364)Natural Science Foundation of Zhejiang(Grant No.LY15A010010)
文摘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.