一类具有凸凹非线性项与Sobolev-Hardy次临界指标的椭圆方程（英文）  

MULTIPLICITY OF POSITIVE SOLUTIONS FOR QUASI-LINEAR ELLIPTIC EQUATIONS INVOLVING CONCAVE-CONVEX NONLINEARITY AND SOBOLEV-HARDY TERM

作　　者：杜明 刘晓春[1] DU Ming;LIU Xiao-chun(School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China)

机构地区：[1]武汉大学数学与统计学院

出　　处：《数学杂志》2019年第5期633-655,共23页Journal of Mathematics

基　　金：Supported by National Natural Science Foundation of China(11371282;11571259)

摘　　要：本文研究了一类具有凸凹非线性项与Sobolev-Hardy次临界指标的椭圆方程.利用Lusternik-Schnirelmann畴数理论以及Nehari流形结构与纤维丛映射的关系,改善了方程在Sobolev空间Wa1,p(RN)中正解的存在性与多重性.In this paper, we investigate the quasi-linear elliptic equations involving concaveconvex nonlinearity and Sobolev-Hardy term. By using the theory of the Lusternik-Schnirelmann category and the relationship between the Nehari manifold and fibering maps, we get some improvement on existence and multiplicity of positive solution.

关 键 词：次临界Sobolev-Hardy指标 NEHARI流形 变号位势 凸凹非线性项 

分 类 号：O175.25[理学—数学]