一类带Hardy-Sobolev临界指数的Kirchhoff型问题的两个正解  

Two Positive Solutions for A Class of Kirchhoff-type Problems with Hardy-Sobolev Critical Exponent

作　　者：廖家锋 朱丽君 陈清方 LIAO Jiafeng;ZHU Lijun;CHEN Qingfang(School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China;College of Mathematics Education,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]西华师范大学数学与信息学院,四川南充637009 [2]西华师范大学公共数学学院,四川南充637009

出　　处：《西华师范大学学报（自然科学版）》2020年第3期268-274,共7页Journal of China West Normal University(Natural Sciences)

基　　金：四川省教育厅自然科学重点资助科研项目(18ZA0471);西华师范大学基本科研业务费项目(18B015,18D052)。

摘　　要：研究了一类带Hardy-Sobolev临界指数的Kirchhoff型问题的多解性,克服了临界指数项导致空间紧性缺失的困难。利用变分方法获得了一个具有负能量的局部极小解和一个具有正能量的山路解。该结果补充完善了带Hardy-Sobolev临界指数的Kirchhoff型问题的多解性结果。In this paper,the multiplicity of positive solutions for a class of Kirchhoff-type problems with Hardy-Sobolev critical exponent is discussed,and the difficulty of lacking compactness caused by critical exponent is solved.A positive minimal solution with nonnegative energy and a positive mountain-pass solution are obtained by the variational method.The results have improved and completed the multiple positive solutions for Kirchhoff-type problem with Hardy-Sobolev critical exponent.

关 键 词：HARDY-SOBOLEV临界指数 Kirchhoff型问题 变分法 正解 

分 类 号：O177.91[理学—数学]