含多重临界位势的渐近线性椭圆方程的正解  

Positive Solution to Asymptotically Linear Elliptic Equation with Multiple Critical Potentials

作　　者：沈尧天[1] 刘爱荣[1] 翟永红 

机构地区：[1]华南理工大学数学科学学院,广东广州510640 [2]广州安迅经济发展有限公司,广东广州510420

出　　处：《华南理工大学学报（自然科学版）》2006年第11期105-108,共4页Journal of South China University of Technology(Natural Science Edition)

基　　金：国家自然科学基金资助项目(10471047)

摘　　要：在新Sobolev-Hardy空间中讨论含多重临界位势的渐近线性椭圆方程正解的存在性.该方程的非线性项是渐近线性的,不满足Ambrosetti-Rabinowitz条件.文中运用没有Palais-Smale条件的山路引理证明了在较弱的条件下,方程至少存在一个正解.This paper discusses the existence of the positive solution to an asymptotically linear elliptic equation with multiple critical potentials in Sobolev.Hardy space. As the right term of the equation is asymptotically linear and does not satisfy the Ambrosetti-Rabinowitz condition, the Mountain Pass Theorem without Palais-Smale condition is used to prove that the equation is of at least one positive solution in a weaker condition.

关 键 词：山路引理 渐近线性 椭圆方程 正解 存在性 强收敛 

分 类 号：O175.25[理学—数学]