一类带Hardy-Sobolev临界指数的奇异Kirchhoff型方程正解的存在性
EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR KIRCHHOFF-TYPE EQUATIONS WITH CRITICAL HARDY-SOBOLEV EXPONENT

本文研究了一类带Hardy-Sobolev临界指数的奇异Kirchhoff型方程 ？-（a+b∫Ω|▽u|2dx） △u=（u5-2s）/（|x|s）+λu-γ，x ∈ Ω， ？u > 0，x∈Ω， ？u=0，x∈？Ω， 其中Ω？R3是一个有界开区域且具有光滑边界？Ω，0∈Ω，a，b ≥ 0且a+b > 0，λ > 0，0 < γ < 1，0 ≤ s < 1.利用变分方法，获得了该问题的一个正局部极小解，补充了文献[1]的结果.
The following singular Kirchhoff-type equations with critical Hardy-Sobolev exponent are considered, ？-(a+b∫Ω|▽u|2dx) △u=(u5-2s)/(|x|s)+λu-γ,x∈Ω, ？u > 0,x ∈Ω, ？u=0,x ∈？Ω, where Ω？R3 is an open bounded domain with smooth boundary ？Ω,0 ∈Ω,a,b ≥ 0 and a+b > 0,λ > 0,0 < γ < 1,0 ≤ s < 1. By the variational methods, the existence of positive local minimal solutions is obtained, which complements the result of[1]