学术交流

应理学院邀请，中南财经政法大学蒋永生教授、嘉兴学院刘海东教授及华中师范大学帅伟副教授将于2023年3月11-12日与我校有关师生进行在线学术研讨，并于11日下午举行线上专题学术报告。

2023年3月11号（周六）下午

点击链接入会，或添加至会议列表：

https://meeting.tencent.com/dm/xNPozSd1p4in

腾讯会议：594-898-884

1.报告人：蒋永生 教授 中南财经政法大学

时间：15:00-16:00

报告题目：Variational analysis of the planar $L_p$ dual Minkowski problem

摘要：In this talk, we consider the planar $L_p$ dual Minkowski problem. By studying the nonlinear problems characterizing the planar $L_p$ dual Minkowski problem in Sobolev spaces, several sharp functional inequalities associated with the $L_p$ dual curvature measures are established to generalize the classical inequalities, such as the Wirtinger's inequality and the Blaschke-Santal\'{o} inequality. Based on these new sharp functional inequalities, various existence results for the planar $L_p$ dual Minkowski problem are obtained for integrable data. Compared with the uniqueness results, the non-uniqueness and multiple $\pi-$periodic solutions are also obtained for $p=0$

through variational analysis. This talk is based on the joint works with Prof. Yong Huang, Prof. Zhengping Wang and Prof. Yonghong Wu.

蒋永生简介：蒋永生，中南财经政法大学教授。研究方向为偏微分方程和非线性泛函分析及其应用。先后获得4项国家自然科学基金项目和1项湖北省自然科学基金项目的资助。研究成果发表在Journal of Function Analysis, Calculus of Variations and Partial Differential Equations，Journal of Differential Equations, Commun.Contemp. Math.,中国科学，数学物理学报等学术期刊上。

2. 报告人：刘海东 教授 嘉兴学院

时间：16:00-17:00

报告题目：Quasilinear Schrodinger equations involving singular potentials

摘要：For the quasilinear Schrodinger equation

$$-\Delta u+V(x)u+\frac{\kappa}{2}\Delta(u^2)u =h(u),\quad u\in H^1(\R^N),$$ where $N\geq 3$, $\kappa$ is a real parameter, $V(x)=V(|x|)$ is a potential allowed to be singular at the origin and $h:\R\to\R$ is a nonlinearity satisfying conditions similar to those in the paper [Arch. Rational Mech. Anal., 82 (1983), 347-375] by H. Berestycki and P.-L. Lions, we establish the existence of infinitely many radial solutions for $\kappa<0$ and the existence of more and more radial solutions as $\kappa\downarrow0$. In the case $\kappa<0$, we allow $h(u)=|u|^{p-2}u$ for $p$ in the whole range $(2, 4N/(N-2))$ and this is in sharp contrast to most of the existing results which are only for $p\in[4, 4N/(N-2))$. Moreover, our result in this case extends the result of H. Berestycki and P.-L. Lions in the paper mentioned above to quasilinear equations with singular potentials. In the case $\kappa\geq 0$, our result extends and covers several related results in the literature, including the result of H. Berestycki and P.-L. Lions. This is a joint work with Dr. Yongtao Jing and Prof. Zhaoli Liu.

刘海东简介：刘海东，嘉兴学院教授，硕士生导师，嘉兴市杰出人才。研究领域为非线性泛函分析与偏微分方程，先后主持国家自然科学基金3项、浙江省自然科学基金2项，在Nonlinearity、Calc. Var. Partial Differential Equations、J. Differential Equations、Proc. Roy. Soc. Edinburgh Sect. A、Discrete Contin. Dys. Syst.、中国科学等期刊发表论文20余篇。

3. 报告人：帅伟 副教授 华中师范大学

时间：17:00-18:00

报告题目：Multiple solutions for logarithmic Schrödinger equations

摘要：In this talk, we discuss the existence of positive ground state solution and least energy sign-changing solution for the logarithmic Schr\"odinger equation. It is known that the corresponding variational functional is not well defined in $H^1(\R^N)$. Via direction derivative and constrained minimization method, we prove the existence of positive ground state solution and least energy sign-changing solution. The existence and multiplicity of solutions for logarithmic Schrodinger equations with potentials are also considered.

帅伟简介：帅伟，华中师范大学副教授，博士生导师。主要研究方向是非线性椭圆型偏微分方程、非线性泛函分析，主持完成国家基金青年项目1项，现主持国家自然科学基金面上项目1项。主要成果发表在J. Funct. Anal., Calc. Var. Partial Differential Equations, Nonlinearity，J. Differential Equations等国际期刊上。