含临界指数项和双重奇异项的Kirchhoff型椭圆边值方程的正解  

Positive Solutions for Kirchhoff-Type Elliptic Boundary Value Equations with Critical Exponent and Double Singular Terms

作　　者：张黔 邓志颖 ZHANG Qian;DENG Zhi-ying(Department of Applied Mathematics,School of Science,Chongqing University of Posts and Telecommunications,Chongqing 400065,China;Chongqing Shulian Mingxin Technology Limited Company,Chongqing 401121,China)

机构地区：[1]重庆邮电大学理学院应用数学系,重庆400065 [2]重庆数联铭信科技有限公司,重庆401121

出　　处：《西南师范大学学报（自然科学版）》2020年第2期11-19,共9页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11471235,11601052,11971339);重庆市基础与前沿研究计划重点项目(cstcjcyjBX0037)

摘　　要：讨论了一类含临界指数项和双重奇异项的Kirchhoff型椭圆边值方程.应用Lions集中紧性原理和Ekeland变分原理,证明了该方程在适当条件下正解的存在性与多重性,推广和改进了一些最近的结果.This paper deals with a class of Kirchhoff-type elliptic boundary value equations involving critical exponent and double singular terms.Based upon the Lions concentration compactness principle and the Ekeland variational principle,we obtain the existence and multiplicity of positive solutions for the problem under the appropriate conditions,some recent results are generalized and significantly improved.

关 键 词：Kirchhoff型方程 SOBOLEV临界指数 奇异项 集中紧性原理 正解 

分 类 号：O175.25[理学—数学]