R^(N)中一类带Hardy-Sobolev临界指数项的Kirchhoff型问题的正解  

Positive Solutions to a Class of Kirchhoff-Type Problems with Hardy-Sobolev Critical Exponent in R^(N)

作　　者：段誉 孙歆 廖家锋 DUAN Yu;SUN Xin;LIAO Jiafeng(College of Science,Guizhou University of Engineering Science,Bijie 551700,Guizhou,China;College of Mathematics Education,China West Normal University,Nanchong 637002,Sichuan,China)

机构地区：[1]贵州工程应用技术学院理学院,贵州毕节551700 [2]西华师范大学公共数学学院,四川南充637002.

出　　处：《数学年刊（A辑）》2023年第3期323-334,共12页Chinese Annals of Mathematics

基　　金：国家自然科学基金(No.11661021);毕节市科学技术项目(No.[2023]28,No.[2023]52)的资助。

摘　　要：研究如下一类带Hardy-Sobolev临界指数的Kirchhoff型问题:{-[a+b(RN|▽u|2dx)m]△u=|u|2(8)-2u/|x|8+λh(x),x∈RN,U∈D1,2(RN),其中N≥3,a,λ≥0,b,㎡>0,0≤δ<2,h∈2/2-1(RN)为非零非负函数。当λ=0时,利用分析技巧获得了问题可解性结果.当λ>0时,利用变分方法获得该问题正解的存在性.特别地,当0<m<2-S/N-2时,获得了问题至少存在两个正解。this article,the following class of Kirchhoff-type problems with Hardy-Sobolev critical exponent is considered{-[a+b(RN|▽u|2dx)m]△u=|u|2(8)-2u/|x|8+λh(x),x∈RN,U∈D1,2(RN)where N≥3,a,λ≥0,b,㎡>0,0≤δ<2,h∈2/2-1(RN)is nonzero and nonnegative.Whenλ=0,some existence results are obtained by some analysis techniques.When^>0,by using the variational method,the existence of positive solutions is obtained.Particularly,when 0<m<2-S/N-2,at least two positive solutions are otained.

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

分 类 号：O177.91[理学—数学]