一类具有临界Sobolev和Hardy-Sobolev指数的椭圆方程的变号解  

Sign-changing Solutions for an Elliptic Equation Involving Critical Sobolev and Hardy-Sobolev Exponent

作　　者：王丽霞 赵萍萍 Wang Lixia;Zhao Pingping(School of Sciences,Tianjin Chengjian University,Tianjin 300384,China)

机构地区：[1]天津城建大学理学院,天津300384

出　　处：《南开大学学报（自然科学版）》2023年第1期61-70,共10页Acta Scientiarum Naturalium Universitatis Nankaiensis

基　　金：Supported by National Natural Science Foundation of China (11801400);Scientific Research Program of Tianjin Education Commission (2020KJ045)。

摘　　要：研究了一类具有临界Sobolev和Hardy-Sobolev指数的椭圆方程的变号解的存在性问题.利用紧性结果、不变集方法和Ljusternik-Schnirelman型的极小极大方法,得到了方程存在无穷多变号解.The existence of sign-changing solution is studied for an elliptic equation involving critical Sobolev exponent and critical Hardy-Sobolev exponent. By using a compactness result, the existence of infinitely many sign-changing solutions are proved by a combination of invariant sets method and Ljusternik-Schnirelman type minimax method.

关 键 词：临界Hardy指数 变号解 临界SOBOLEV指数 

分 类 号：O175.25[理学—数学]