Normalized solutions of Kirchhoff type equations

发布时间:2022年12月02日 作者:陈思彤   阅读次数:[]

报告题目:Normalized solutions of Kirchhoff type equations




报告摘要:In this talk, we are concerned with the existence, non-existence and multiplicity of positive normalized solutions (λ_c,u_c )∈R×H^1 (R^N) to the following Kirchhoff problem

-(a+b∫_(R^N)▒〖|∇u|^2 dx〗)Δu+λu=g(u),x∈R^N,N≥1

satisfying the normalization constraint ∫_(R^N)▒〖|u|^2 dx=c〗>0. The nonlinearity g is allowed to be subcritical or critical at infinity. In particular, the higher dimension case N≥5 is also considered and such problems lack the mountain pass geometry due to the presence of the non-local term ∫_(R^N)▒〖|∇u|^2 dx〗. This talk is based on joint works with Xiaoyu Zeng(WUT), Yimin Zhang(WUT), Jian Zhang(UPC) and Xuexiu Zhong(SCNU).

报告人简介:张建军,重庆交通大学数学与统计学院教授,重庆市数学会副理事长。2001年本科毕业于中国矿业大学数学系,2012年于清华大学数学科学系获博士学位,2018年获得意大利副教授国家资格认证,2020年入选重庆市高校中青年骨干教师,主持国家自然科学基金面上项目、国际(地区)合作交流项目和意大利伦巴第研究员基金(Global ERC)各1项。在非线性薛定谔方程的半经典状态和规范化解的研究等方面取得了一些重要结果并发表在国际主流学术刊物上,如Communications in Partial Differential Equations,Journal of Differential Equations, Calculus of Variations and Partial Differential Equations, Nonlinearity, Proceedings of the Royal Society of Edinburgh, Section A Mathematics, Journal of the London Mathematical Society等。

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