In this talk, we explore the existence of fully nontrivial solutions to the nonlinear Brezis-Nirenberg Maxwell system. This system originates from the time-harmonic Maxwell equations and possesses a variational structure. We address both general subcritical cases and Sobolev critical cases, establishing the existence of a fully nontrivial ground state solution with cylindrical symmetry. Additionally, we prove several properties of these solutions. To achieve this, we develop a new critical point theory that not only resolves the current problem but also facilitates the treatment of more general anisotropic media and other variational problems. Notably, our results provide a positive answer to the open problem posed by T. Bartsch and J. Mederski in early paper.

王俊，现为江苏大学教授、博士生导师，数学科学学院副院长。2011年东南大学博士毕业，2014年晋升为副教授，2015年晋升为博导，2018年破格晋升为教授。曾获江苏省杰青，“全国百篇优秀博士论文提名论文”，首届江苏省优青、江苏省“333高层次人才”中青年学科带头人和“六大人才高峰”人才项目等， 2019年获教育部自然科学二等奖（第二完成人）。主持国家面上项目3项、参与国家重点研发计划“数学与应用数学”专项变分理论与 Yang-Mills方程1项，主持国家青年基金及其他省部级项目6项。 现为美国数学会《Math. Review》和德国《zbMATH》评论员。主要从事非线性泛函分析与偏微分方程和应用数学的研究，在Comm. Partial Differential Equations，Math. Z, Journal of Functional Analysis, Ann. Sc. Norm. Super. Pisa, Calculus of Variations and Partial Differential Equations, Annales Henri Poincare，Nonlinearity, J. Math. Fluid Mech.和Journal of Differential Equations等国际数学专业杂志上发表SCI论文80多篇。曾在中国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，中国香港理工大学、澳门大学，澳大利亚麦考瑞大学，悉尼大学和新英格兰大学等高校。