带有临界Sobolev和Hardy项的半线性椭圆方程的解(Ⅰ)(英文)

Solutions for Semilinear Elliptic Equations with Critical Sobolev and Hardy Terms(Ⅰ)

设ΩRN是有界光滑区域,0∈,ΩN≥3,2*:=2NN-2,0≤s<2,2*(s):=2(N-s)N-2,2<r<2*(s).对于满足一定条件的参数λ和μ,证明了带D irich let边界条件的奇异椭圆问题-Δu-μu x 2=u 2*-2u+λu

Let Ωbelong to R^N be a smooth bounded domain such that 0 ∈Ω ,N≥3,2^＊：=2N/N-2,0≤s〈2,2^＊（s）：=2（N-s）/N-2,2〈r〈2^＊（s）.We prove some crucial properties of the singular critical problem-△u-μu/｜x｜^2=｜u｜^2＋-2u＋λ｜u｜^r-2/｜x｜^1uwith Diriehlet boundary eondition on Ω for suitable positive parameters λ and μ.