报告时间：2023/04/17 09:00-

报告地点：格物楼数学研究中心报告厅

报告题目：Existence and multiplicity of positive solutions for some elliptic equations on the graphs

报告摘要：In this talk, we introduce the Mean field equation and the relativistic Abelian Chern-Simons equations (involving two Higgs particles and any two gauge fields) on the finite connected graphs. For the former equation, we establish the existence results and some uniqueness result. In particular, we find that there is no set of critical parameters for the Mean field equation on the finite graphs and the existence is ensured for any non-negative parameters, which is in contrast to the continuous case. In addition, we give the optimal constant which is the threshold for the uniqueness of the equation on the finite complete graphs with simple weight. Finally, we give the existence and nonexistence of a Minimizer for Thomas-Fermi- Dirac-von Weizsacker Model on lattice graph. 

报告人简介：王俊，男，江苏大学教授，博士生导师，现任数学科学学院副经理。东南大学博士毕业，2018年破格晋升为教授。曾获“全国百篇优秀博士论文”提名论文，2020年获江苏省杰青，2019年获教育部高等学校科学研究优秀成果奖（自然科学类）二等奖。曾在台湾大学从事博士后研究工作，并先后应邀访问美国威廉玛丽学院和香港理工大学等高校。主持国家面上项目2项，参与国家重点研发计划“数学与应用数学”专项1项，主持完成国家自然科学基金青年和省部级项目6项。长期从事变分方法与非线性偏微分方程的研究，在CPDE, JFA, CVPDE, Nonlinearity和JDE等国际数学专业杂志上发表多篇科研论文。