含临界指数的一类p-Laplacian奇异拟线性椭圆方程组正基态解的存在性  

The Existence of Positive Ground State Solutions for a Singular Quasilinear Elliptic Systems Involving Critical Exponents

作　　者：张文丽[1] 

机构地区：[1]长治学院数学系,山西长治046011

出　　处：《数学的实践与认识》2014年第21期286-295,共10页Mathematics in Practice and Theory

基　　金：山西省高校科技研究开发项目(20111129;2013158)

摘　　要：研究了一类含Sobolev临界指数的p-Laplacian奇异拟线性椭圆方程组,利用变分方法,结合Nehari流形和集中紧性原理证明对应的能量泛函满足局部(PS)条件,得到了这一方程组正基态解的存在性.In the paper,a singular quasilinear elliptic systems involving Sobolev critical exponents are studied.By using the variational method, together with Nehari manifold and concentration compactness principle, the existence of a positive ground state solution was proved for the systems by proving that the energy functional corresponding to the systems satisfies the （PS） condition.

关 键 词：基态解 奇异拟线性椭圆方程组 NEHARI流形 集中紧性原理 SOBOLEV临界指数 

分 类 号：O175.25[理学—数学]