一类带有不同Rellich项的临界双调和方程组的非平凡解  

Biharmonic Systems Involving Critical Nonlinearities and Different Rellich-Type Potentials

作　　者：康东升[1] 熊萍 Kang Dongsheng;Xiong Ping(School of Mathematics and Statistics, South-Central University for Nationalities, Wuhan 43007)

机构地区：[1]中南民族大学数学与统计学学院,武汉430074

出　　处：《数学物理学报（A辑）》2017年第6期1105-1118,共14页Acta Mathematica Scientia

基　　金：中南民族大学中央高校基本科研业务费资金(CZP17015)~~

摘　　要：该文研究一类带有多重临界Sobolev指数和不同Rellich位势项的双调和方程组.利用变分法得到在一定条件下相关最佳常数的达到函数对的存在形式和基本性质,并证明双调和方程组非平凡解的存在性.In this paper, a system of biharmonic equations is investigated, which involves multiple critical Sobolev nonlinearities and different Rellich-type terms. The minimizers of the related best Soblev constant are found under certain assumptions and the existence of solutions to the system is established by variational arguments.

关 键 词：双调和方程组 解 临界SOBOLEV指数 Rellich位势项 变分法 

分 类 号：O175.25[理学—数学]