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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
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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.
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 天津城建大学理学院
出处 《南开大学学报（自然科学版）》 CAS CSCD 北大核心 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)。
关键词 临界Hardy指数 变号解 临界SOBOLEV指数 critical Hardy exponent sign-changing solutions critical Sobolev exponent
分类号 O175.25 [理学—基础数学]
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南开大学学报（自然科学版）
2023年 第1期

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