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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)

发布者:戴 情   发布时间:2022-04-25  浏览次数:10

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2022428日(周四)1900-2200

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 EquationsMath. Z. NonlinearityJ. Differential EquationsDiscrete 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