主講人：葉東 華東師范大學(xué)教授
時(shí)間：2024年6月18日14：00
地點(diǎn)：三號(hào)樓332室
舉辦單位：數(shù)理學(xué)院
主講人介紹：葉東，現(xiàn)任華東師范大學(xué)數(shù)學(xué)科學(xué)學(xué)院教授。1990年畢業(yè)于武漢大學(xué)中法數(shù)學(xué)班，1994年在法國(guó)卡尚高等師范學(xué)院獲得博士學(xué)位，后長(zhǎng)期在法國(guó)大學(xué)任職，回國(guó)前是法國(guó)洛林大學(xué)的一級(jí)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(guó)家級(jí)高層次人才計(jì)劃，于當(dāng)年9月全職回到華東師范大學(xué)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.