R^3中一类带临界指数的Kirchhoff型问题的注记  

Remark on a Class of Kirchhoff-Type Problem with Critical Exponent in R^3

作　　者：伍君芬 李红英 WU Jun-fen;LI Hong-ying(Department of Scientific Education,Collage of Mobile Telecommunications,Chongqing Universityof Posts and Telecom,Hechuan Chongqing 401520,China;School of Mathematics and Information,China West Normal University,Nanchong Sichuan 637009,China)

机构地区：[1]重庆邮电大学移通学院数理教学部,重庆合川401520 [2]西华师范大学数学与信息学院,四川南充637009

出　　处：《西南师范大学学报（自然科学版）》2019年第6期27-30,共4页Journal of Southwest China Normal University(Natural Science Edition)

基　　金：重庆邮电大学移通学院高等教育教学改革研究项目(YTJG201722);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项目(18D052);西华师范大学创新团队项目(CXTD2018-8)

摘　　要：研究如下一类带临界指数的Kirchhoff型问题:{-a+b∫R^3|u|^2dxΔu=u^5+λk(x)uq-1 x∈R^3u∈D^1,2(R^3)其中a,b,λ>0,2<q<6,k∈L6/6-q(R^3)为非零非负函数.利用变分方法,获得了一个正山路解.进一步,证明了正基态解的存在性.补充并完善了近期相关文献的结果.In this paper, the following Kirchhoff-type problem with critical exponent is considered:- a+b∫ R^3 | u|^ d x Δ u=u^5 +λk(x)u^ q-1 x∈ R 3 u∈D^1,2 ( R^3 ) where a,b,λ>0, 2<q<6, k∈L 6/-q ( R^3 ) is nonzero and nonnegative. By using the variational method, a positive Moutian-Pass solution is obtained and the existence of positive ground state solution is proved, which complete and improve some results of the recent reference.

关 键 词：临界指数 Kirchhoff型问题 变分法 正解 

分 类 号：O176.3[理学—数学]