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# 数学学科现代分析及其应用研究所（Claudianor O. Alves 教授 巴西大坎皮纳联邦大学）

 报告题目：On existence of multiple normalized solutions to a class of elliptic problems in whole $\mathbb{R}^N$ via Lusternik-Schnirelman category报告人：Claudianor O. Alves 教授（巴西大坎皮纳联邦大学）报告时间：2022年4月28日（周四）19：00-22：00报告地点：腾讯会议ID:  786-936-218摘要：In this seminary, we will talk about the existence of multiple  normalized solutions  to the following class of elliptic problems        \begin{align*}       \left\{       \begin{aligned}       &-\Delta u+V(\epsilon x)u=\lambda u+f(u), \quad       \quad       \hbox{in }\mathbb{R}^N,\\       &\int_{\mathbb{R}^{N}}|u|^{2}dx=a^{2},       \end{aligned}       \right.       \end{align*}where $a,\epsilon>0$, $\lambda\in \mathbb{R}$ is an unknown parameter that appears as a Lagrange multiplier, $V:\mathbb{R}^N \to [0,\infty)$ is a continuous function, and $f$ is continuous function with $L^2$-subcritical growth. It is proved that the numbers of normalized solutions are related to the topology of the set where the potential $V$ attains its minimum value. In the proof our main result we apply minimization techniques and LjusternikSchnirelmann theory. This is a joint work with Nguyen Van Thin.报告人简介：Claudianor O. Alves，巴西大坎皮纳联邦大学教授，是国际著名非线性分析研究领域的专家，已在 Proc. Amer. Math.Soc.，Calc. Var. Partial Differential Equations，Math. Z.， Nonlinearity，J. Differential Equations，Discrete Contin. Dyn. Syst. 等国际高水平数学刊物上发表论文200余篇论文。  邀请人：非线性分析与PDE团队  