一类涉及分数阶Hardy-Schrödinger算子和Hardy-Sobolev临界指数的方程组  

A system involving fractional Hardy-Schrödinger operators and critical Hardy-Sobolev exponents

作　　者：郭振宇 刘敏 唐仲伟[2] Zhenyu Guo;Min Liu;Zhongwei Tang

机构地区：[1]辽宁师范大学数学学院,大连116029 [2]北京师范大学数学科学学院,北京100875

出　　处：《中国科学：数学》2021年第5期697-710,共14页Scientia Sinica：Mathematica

基　　金：国家自然科学基金(批准号:11701248,11571040和11671331);辽宁省自然科学基金(批准号:20180540028)资助项目。

摘　　要：本文研究一类涉及分数阶Hardy-Schrödinger算子和Hardy-Sobolev临界指数的方程组.在适当的条件下,本文获得该方程组基态解的存在性和相关性结果.为克服紧性缺失,本文考虑一个定义在有界区域上的次临界辅助问题,并证得该辅助问题对应的紧嵌入性结论.We study a system involving fractional Hardy-Schrödinger operators and critical Hardy-Sobolev exponents.Under appropriate conditions,the existence and correlation results of ground state solutions to this system are obtained.To overcome the lack of compactness,we consider a proper approximate problem with subcritical nonlinear terms de ned in a bounded domain.Moreover,a compact embedding result for the approximate problem is proved.

关 键 词：基态解 分数阶Hardy-Schrödinger算子 分数阶Hardy-Sobolev临界指数 

分 类 号：O175[理学—数学]