主講人：葉東 華東師范大學教授

時間：2024年6月18日14：00

地點：三號樓332室

舉辦單位：數(shù)理學院

主講人介紹：葉東，現(xiàn)任華東師范大學數(shù)學科學學院教授。1990年畢業(yè)于武漢大學中法數(shù)學班，1994年在法國卡尚高等師范學院獲得博士學位，后長期在法國大學任職，回國前是法國洛林大學的一級教授。主要研究領(lǐng)域是非線性偏微分方程和幾何分析。2018年入選國家級高層次人才計劃，于當年9月全職回到華東師范大學工作。

內(nèi)容介紹：We consider a nonlinear Schr\odinger system in ${\mathbb R}^3$: \begin{align*} -\Delta u_j +P_j(x) u=\mu_j u_j^3+\sum\limits_{i=1,i\neq j}^N\beta_{ij}u_i^2u_j, \end{align*} where $N\geq3$, $P_j$ are nonnegative radial potentials; $\mu_j>0$, $\beta_{ij}=\beta_{ji}$ are coupling constants. This type of systems has been widely studied in the last decade, many purely synchronized or segregated solutions are constructed, but few considerations for simultaneous synchronized and segregated solutions exist. On the other hand, there are new challenges in dealing with the existence of multiple sign-changing solutions or semi-nodal solutions. Using Lyapunov-Schmidt reduction method, we construct new type of positive and sign-changing solutions with simultaneous synchronization and segregation. We prove the existence of infinitely many non-radial positive or also sign-changing vector solutions, where some components are synchronized but segregated with other components; the energy level can be arbitrarily large; and our approach works for general any number of components $N \geq 3$. This is a joint work with Qingfang Wang.