报告题目：Analysis and simulations of Maxwell's equations in PMLs and graphene

报告人：美国内华达大学拉斯维加斯分校李继春教授

报告时间：2024年1月11日10:00--11:00

报告地点：立志楼A422

摘要：In this talk, we will introduce some results on the positive solutions for some nonlinear discrete Dirichlet boundary value problems with the mean curvature operator by using critical point theory. First, some sufficient conditions on the existence of infinitely many positive solutions are given. We show that, the suitable oscillating behavior of the nonlinear term near at the origin and at infinity will lead to the existence of a sequence of pairwise distinct nontrivial positive solutions. Then, the existence of at least two positive solutions is established when the nonlinear term is not oscillatory both at the origin and at infinity. Examples are also given to illustrate our main results at last.

李继春: 美国内华达大学拉斯维加斯分校教授，应用数学与统计中心主任,担任德克萨斯大学奥斯汀分校博士后研究员和加州大学洛杉矶分校应用数学研究所（IPAM）副所长。研究领域包括有限元方法、高阶紧差分方法、RBF无网格方法以及偏微分方程的应用。发表SCI论文140余篇，专著2部。在2022年Research.com 全美前1000名数学家排名中位列第965位，全世界数学家排第2261位。目前，担任《Results in Applied Mathematics》的主编，《Computers and Mathematics with Applications》的执行主编。