含Sobolev-Hardy位势的非线性椭圆方程正解的存在性  

Existence of Positive Solutions for the Elliptic Problems Involving Sobolev-Hardy Potential

作　　者：韩亚蝶[1] 李佳[1] 杨婵[1] 姚仰新[1] 

机构地区：[1]华南理工大学理学院数学系,广东广州510640

出　　处：《内蒙古师范大学学报（自然科学汉文版）》2011年第6期570-574,共5页Journal of Inner Mongolia Normal University(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10771074)

摘　　要：研究了具Caffarelli-Kohn-Nirenberg不等式类型及Hardy位势的非线性椭圆问题,通过对参数的合理设定,利用临界点理论上的变分方法及山路引理,证明了该问题至少存在一个正解.In this paper,a nonlinear elliptic problem with the type of Caffarelli-Kohn-Nirenberg inequalities and Hardy potential will be studied. We will prove that the problem has at least a positive solution, by the Mountain Pass Theorem and the variational methods based on the critical point theory. Moreover,the parameters should be set reasonably.

关 键 词：Caffarelli-Kohn-Nirenberg不等式 椭圆方程 正解 

分 类 号：O175.25[理学—数学]