报告题目：Multiple solutions for 1-D quasilinear indefinite Schrodinger equations

主讲人：刘轼波教授 (弗罗里达理工学院)

报告时间：2024年11月18日, 上午9:00-10:30

报告地点：数学科学学院301室，腾讯会议：110 724 531

报告摘要：Quasilinear stationary Schrödinger equations have attracted great interest in the community of nonlinear analysis since 2002. Most results in the literature require that the Schrödinger operator is positive. The first result for the indefinite case is due to Liu & Zhou [J. Differential Equations 265 (2018)], where the potential is coercive, so that the working space can be compactly embedded. In this talk, using variational methods we study the one-dimensional quasilinear Schrödinger equations with bounded indefinite potential. We obtain existence and multiplicity results for this problem. It should be pointed out that unlike many noncompact variational problems, the weak limits of Palais-Smale sequences may not be critical points of the variational functional.

主讲人简介：刘轼波，美国佛罗里达理工学院教授、博士生导师。2003年于中国科学院数学与系统科学研究院数学所获得理学博士学位，2005年在北京大学完成博士后研究，历任汕头大学教授、厦门大学数学系教授，2022年到美国佛罗里达理工学院(Florida Institute of Technology)工作。长期从事非线性泛函分析、临界点理论及非线性微分方程的多重解的研究，至今已经在国际重要数学期刊发表论文50余篇，主持4项国家自然科学基金项目。