带有多重临界指标和Hardy项的椭圆方程组的基态解  

Ground State Solutions for Elliptic Systems Involving Multiple Critical Exponents and Hardy Terms

作　　者：康东升[1] 李智萍[1] 

机构地区：[1]中南民族大学数学与统计学学院,湖北武汉430074

出　　处：《应用数学》2013年第3期698-705,共8页Mathematica Applicata

基　　金：国家自然科学基金(10771219)

摘　　要：本文利用变分方法和分析技巧,研究一类带有多重临界指标和Hardy位势项的椭圆方程组,证明方程组基态解的存在性,估计基态解的能量和节点域数量.In this paper,a system of elliptic equations is investigated, which involves mul- tiple critical Sobolev exponents and Hardy-type terms. By variational methods and analytic techniques,the existence of ground state solution to the system is established. Moreover,we give energy estimates and number of nodal domains for these ground state solutions.

关 键 词：椭圆方程组 基态解 节点域 临界指数 HARDY位势 非平凡解 变分方法 

分 类 号：O175.25[理学—数学]