| 摘要: |
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. |
| 关键词: Kirchhoff型方程 Hardy-Sobolev临界指数 奇异 变分方法 |
| DOI： |
| 分类号:O175.25 |
| 基金项目:贵州省科技厅联合基金项目（黔科合LH字[2016]7033）；贵州省教育厅创新群体重大研究项目（黔教合KY[2016]046）；西华师范大学英才科研基金资金项目（17YC383）；西华师范大学基本科研业务费资金项目（16E014））. |
|
| EXISTENCE OF POSITIVE SOLUTIONS FOR A CLASS OF SINGULAR KIRCHHOFF-TYPE EQUATIONS WITH CRITICAL HARDY-SOBOLEV EXPONENT |
|
CHEN Ming1, ZHANG Peng1, LIAO Jia-feng2
|
|
1.School of Mathematics, Zunyi Normal College, Zunyi 563006, China;2.School of Mathematics and Information, China West Normal University, Nanchong 637002, China
|
| Abstract: |
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]. |
| Key words: Kirchhoff-type equation critical Hardy-Sobolev exponent singularity variational method |
