带有Hardy-Sobolev临界指数的椭圆型方程解的存在性  

Existence of Solutions for Elliptic Equations with Hardy-Sobolev Critical Exponents

作　　者：杨帆 王琳琳 YANG Fan;WANG Linlin(School of Mathematics and Statistics Science,Ludong University,Yantai 264039,China)

机构地区：[1]鲁东大学数学与统计科学学院,山东烟台264039

出　　处：《烟台大学学报（自然科学与工程版）》2023年第4期393-398,共6页Journal of Yantai University(Natural Science and Engineering Edition)

基　　金：国家自然科学基金资助项目(11201213)。

摘　　要：研究带有Hardy项和Hardy-Sobolev临界指数项的奇异型椭圆型方程解的存在性,在某些确定的条件下,运用Hardy不等式,Hardy-Sobolev不等式以及变分理论中的山路引理证明了非平凡解的存在性。The existence of solutions of a singular elliptic equation with Hardy term and Hardy-Sobolev critical exponents is studied.Under certain conditions,the existence of nontrivial solutions is proved by using Hardy inequality,Hardy-Sobolev inequality and Mountain Pass Lemma in variational theory.

关 键 词：椭圆型方程 解的存在性 山路引理 

分 类 号：O175.2[理学—数学]