走向现代数学学术报告 - 李本鸟副教授（No. 816)

报告题目：Existence and non-existence of clustering peak solutions for Schr\"{o}dinger systems

报告时间：2025年10月25日 8:20

报告地点：东海岸校区-D实209

报 告 人：李本鸟 副教授（江西师范大学）

邀 请 人：王大斌 教授

报告摘要：In this talk, I will introduce some existence results on the nonlinear Schr\"{o}dinger system. Applying Lyapunov-Schmidt reduction method and topological degree theory, we show the existence of clustering peak solutions concentrating at saddle points of the potentials. Remarkably, the characteristics of energy functionals exhibit significant differences between the saddle point case and the local maximum case, and thus a series of subtle difficulties arise. Moreover, we also prove the non-existence of clustering peak solutions with all peaks concentrating at local minimum points of the potentials. This work is joint with Yuke He, Wei Long and Weilin Yu.

报告人简介：李本鸟，江西师范大学副教授，博士毕业于澳大利亚新英格兰大学，之后在澳大利亚新英格兰大学做博士后研究。主要研究二阶椭圆方程解的存在性和唯一性问题，在Ann. Sc.Norm. Super. Pisa Cl. Sci.，Calc. Var. PDE, J. Differential Equations，Comm. Contem. Math, Sci. China Math.等国际知名学术期刊上发表多篇学术论文。主持国家自然科学基金项目3项。