Recent results on the number of positive solutions of an elliptic system

主讲人：刘兆理 首都师范大学教授

时间：2025年4月18日16：00

地点：三号楼332室

举办单位：数理学院

主讲人介绍：刘兆理，曾任山东大学数学学院教授，现任首都师范大学数学科学学院教授，从事非线性分析方向的研究，发展了下降流不变集方法，在非线性椭圆型方程解的存在性方面获得多项有意义的研究成果。曾获得国家杰出青年科学基金、4项省部级科研一等奖和二等奖、北京市首批高层次人才称号、首都劳动奖章、北京市优秀博士学位论文指导教师称号。目前担任国内外6个数学期刊的编委。

内容介绍：In this presentation, I will discuss recent advances in determining the number of positive solutions for a particular elliptic system. This system arises naturally in several important physical models, including Bose-Einstein condensate theory and nonlinear optics. Our findings reveal several interesting phenomena: the existence of multiple positive solutions in certain parameter regimes, precise solution counts in specific cases, and the monotonic dependence of solution numbers on system parameters across different regions. This is joint work with Yongtao Jing, Fanqin Liu, Haidong Liu, Yanyan Liu, Juncheng Wei, Zhangjian Yan.