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

报告时间：2025年11月17日（星期一） 20:00-21:00

报告地点：腾讯会议ID：844-561-879

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University of New England. 主要研究方向是非线性椭圆微分方程爆破解及集中解的性质，如存在性、唯一性、非退化性等。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。