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王春花:Multi-peak Positive Solutions to a Class of Kirchhoff Equations(时间:12.7)

发布日期:2020-12-04  作者:刘敏  浏览数:

报告人:王春花 华中师范大学副教授

报告时间:12月7日15:00

报告地点:腾讯会议号:500 887 139

主办单位:数学与统计学院

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  We mainly consider a nonlocal Kirchhoff problem with a small parameter. Under some mild assumptions on the potential function, we obtain multi-peak solutions for the parameter sufficiently small by Lyapunov-Schmidt reduction method. Even though many results on single peak solutions to singularly perturbed Kirchhoff problems have been derived by various methods, there exist no results on multi-peak solutions before our work, due to some difficulties caused by the nonlocal term. A remarkable new feature of this problem is that the corresponding unperturbed problem turns out to be a system of partial differential equations, but not a single Kirchhoff equation, which is quite different from most of elliptic singular perturbation problems. This is based on a joint work with Peng Luo, Prof. Shuangjie Peng and   Changlin Xiang.

  王春花,华中师范大学副教授、硕士生导师。主要从事非线性椭圆方程(组)解的存在性及解的性态、非线性泛函分析等研究。在国际刊物上发表SCI论文30余篇,主持国家课题青年基金一项、面上项目两项。其部分研究成果发表在 J. Funct. Anal.、Calc. Var. Partial Differential Equations J. Differential Equations等刊物上。