报告题目：On the Krein-Rutman Theorem: A Simple Dynamical Approach and its Generalizations

报告人：李德生 教授 天津大学

邀请人：吴事良教授

报告时间：2024年6月12日（周三） 14:30

腾讯会议ID：176 646 150 密码：123456

报告人简介： 李德生，天津大学数学学院教授，博士生导师。主要从事动力系统和非线性微分方程方面的研究工作，研究兴趣包括动力系统的Morse理论、Conley指标、大范围动态分支理论、主特征值问题等；主持承担国家自然科学基金项目6项；在国内外著名数学期刊《Ind. Univ. Math. J.》、《J. Diff. Eqns.》、《SIAM J. Cont. Optim.》、《SIAM J. Appl. Dyna. Syst.》等杂志发表论文50余篇。

摘要：In this talk I will introduce a very simple dynamical approach towards the classical Perron-Frobenius theory and Krein-Rutman Theorem concerning the first principal eigenvalue problems of positive operators by using only some elementary knowledge on linear ODEs. This approach was developed recently by myself and my PhD students, which is completely self-contained and significantly different from those in the literature. It gives a nearly pure dynamical insight into the remarkable theory. As a result, a generalized complex version of the theory is obtained for both bounded and unbounded operators. The application to a general elliptic operator under mixed boundary-value condition will also be addressed.