全空间中带有不同Hardy项的临界椭圆方程组的基态解  

Ground State Solution to Critical Elliptic Systems Involving Different Hardy-Type Terms in the Whole Space

作　　者：康东升[1] 段笑 龚睫茜 

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《中南民族大学学报（自然科学版）》2016年第3期141-145,共5页Journal of South-Central University for Nationalities：Natural Science Edition

基　　金：国家自然科学基金资助项目(11601530)

摘　　要：研究了带有不同Hardy项的非线性临界椭圆方程组以及与Rayleigh商相关的极小值问题,运用变分原理和分析技巧,证明了Hardy项系数分别为常系数和变系数时方程组正基态解的存在性.In this paper, nonlinear critical elliptic systems involving different Hardy-type terms were investigated and the minimizers to Rayleigh quotients were studied. By variational methods and analytical techniques, the existence of positive ground state solutions to the systems was verified, where the coefficients of Hardy-type terms are constants and functions respectively.

关 键 词：椭圆方程组 基态解 变分法 RAYLEIGH商 

分 类 号：O175.25[理学—数学]