应304am永利集团官网王智诚教授和孙建文副教授的邀请，南开大学马世旺教授将于2022年12月14日-12月15日与我校有关师生进行在线学术研讨，其中12月15日举行线上专题学术报告。

报告题目: Existence and asymptotic behavior of normalized solutions for Choquard type equations

时 间：12月15日9:00.

腾讯会议ID：384-411-384

报告摘要：In this talk, we prensent some resent results on the existence and multiplicity of normalized solutions of the nonlinear Choquard equation$$-\Delta u+\lambda u=(I_\alpha \ast F(u))F’(u), \quad {\rm in} \ \mathbb R^N, \eqno(Ch) $$ under the normalization constraint $\int_{\mathbb R^N}|u|^2=c^2$, where $N\ge 3$ is an integer, $I_\alpha$ is the Riesz potential and the frequency $\lambda\in \mathbb R$ appears as a Lagrange multiplier. For a class of Choquard type equations with combined nonlinearities, we first fix the frequency $\lambda$ and study the asymptotic behavior of positive ground state solutions $u_\lambda$ as $\lambda \to 0$ (resp. $\lambda \to \infty$). We prove that after {\em a suitable rescaling} the ground state solutions $u_\lambda$ converge in $H^1(\mathbb R^N)$ to a particular solution of some limit equations. We also establish a sharp asymptotic characterisation of such a rescaling, an optimal uniform decay estimates of ground states $u_\lambda$ and the exact asymptotic expression of $\|u_\lambda\|_2^2$. Applying the above conclusions to the associated mass constrained problem with normalization constraint $\int_{\mathbb R^N}|u|^2=c^2$, we obtain the existence, multiplicity and exact asymptotic behavior of positive normalized solutions of such a problem as $c\to 0$ and $c\to \infty$.

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马世旺教授简介

马世旺，南开大学数学学院教授、博士生导师。1997年于湖南大学获理学博士学位，先后工作于上海交通大学、南开大学。已主持完成国家自然科学基金项目5项、高等学校博士学科点专项科研基金项目1项。研究领域为非线性分析、微分方程与动力系统，在J. Differential Equations、CVPDE、 J. Dynam. Differential Equations，中国科学等国内外权威数学期刊发表学术论文90余篇，数学评论显示，研究成果已被引用1000多次，单篇引用超过200次。

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2022年12月9日