报告题目：The Existence and Non-degeneracy of the Dichotomous peak-solutions to the nonlinear Schr\"odiner systems

报  告 人： 王春花

时     间：2024年7月2号上午10：00--11：00

地    点：腾讯会议（会议号：530486833）

摘   要：We are concerned with the following nonlinear Schr\"odiner system\begin{equation*}\begin{cases}-\epsilon^{2}\Delta u +P_1(x) u= \mu_1 u^3 +\beta uv^2,&~\text{in}\;\mathbb R^3,\\\noalign{\vskip1truemm} -\epsilon^{2}\Delta v+P_2(x) v= \mu_2 v^3 +\betau^2v, &~\text{in}\;\mathbb R^3,\end{cases}\end{equation*}where $\epsilon$ is a positive parameter, $P_{i}(x)(i=1,2)$ are the potential functions, $\mu_1>0$, $\mu_2>0$ and $\beta\in\mathbb R$ is a coupling constant. Employing the finite dimensional reduction method, we prove that there are infinitely many synchronized and segregated dichotomous peak solutions which concentrate both in a bounded domain and near infinity. Moreover, by applying the local Pohozaev identities, we prove that the dichotomous peak-solutions of synchronized type are non-degenerate.

报告人简介：

王春花，华中师范大学数学与统计学学院副教授，博士生导师。主持多项国家自然科学基金。主要研究方向：非线性偏微分方程和非线性泛函分析。相关研究成果发表在JFA、CVPDE、JDE等在内的重要学术期刊。