一类临界奇异Kirchhoff型椭圆边值问题的正解  

On Positive Solutions for a Class of Critical Singular Kirchhoff-Type Elliptic Boundary Value Problems

作　　者：樊洪森 邓志颖 FAN Hong-Sen;DENG Zhi-Ying(School of Science, Chongqing University of Posts and Telecommunications, Chongqing 400065, China)

机构地区：[1]重庆邮电大学理学院,重庆400065

出　　处：《西南师范大学学报（自然科学版）》2021年第6期27-35,共9页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：国家自然科学基金项目(11971339,11601052);重庆邮电大学金课基金项目(XJKXX20201-15).

摘　　要：讨论了一类带Sobolev-Hardy临界指数项的Kirchhoff型椭圆边值问题,应用Nehari流形、纤维映射和Brezis-Lieb引理等方法,证明了该问题在一定条件下正解的存在性,推广和改进了最近的一些结果.This paper deals with a class of Kirchhoff-type elliptic boundary value equations involving the critical Sobolev-Hardy exponents.Based upon the Nehari manifold,fiber mapping,and Brezis-Lieb lemma etc,the existence of positive solutions for the problem has been obtained under the appropriate conditions,and some recent results been generalized and significantly improved.

关 键 词：正解 SOBOLEV-HARDY临界指数 NEHARI流形 Kirchhoff型问题 

分 类 号：O175.25[理学—数学]