报告时间：2024年4月26日（星期五）11：00-12：00

报告地点：翡翠科教楼B1710

报告人：钟学秀 副研究员

工作单位：华南师范大学

举办单位：英国威廉希尔公司

报告简介：

In this talk, we are concerned with system of m p-Laplacian Schr\"odinger equations with competition interactions in a bounded regular domain. When the nonlinearities are odd satisfying some suitable assumptions, we can apply the vector genus and descending flow method to establish infinitely many sign-changing normalized solutions. The innovation is that we construct a tangent pseudo-gradient vector field for the energy functional on the constrained manifold, which can be used to find invariant sets of descending flow. The difficulty is reinforced by the p-Laplacian operator and also by the normalized constraint. Since we are dealing with $p>1$ in a unified way, the energy functional may be not regular enough and the p-Laplacian operator is not linear, we cannot benefit from certain classical techniques directly. This is a joint work with Prof. Jianjun Zhang and my students Anjie Feng and Jinfang Zhou.

报告人简介：

钟学秀，华南师范大学副研究员，华南数学应用与交叉研究中心青年拔尖引进人才，最新ESI高被引学者。研究方向为运用非线性分析、变分法等方法来研究几何分析学、数学物理中椭圆型偏微分方程和方程组以及某些不等式问题。主持国家青年基金和面上基金各一项。已在J.Differential Geom.， J. Math. Pures Appl., Math. Ann.， Ann. Sc. Norm. Super. Pisa Cl. Sci. (5)，Calc. Var. PDE，J. Differential Equations等国际重要刊物上发表多篇学术论文。在非线性泛函分析和椭圆偏微分方程领域的Li-Lin 公开问题，Sirakov 公开问题，Bartsch-Jeanjean-Soave公开问题等方面获得了重要进展。