报告题目 ：Local linking anbd indefinite Schrodinger equations

报告人：刘轼波教授（厦门大学）

报告地点：理学实验楼312报告厅

报告时间：2019年4月30日下午 2：30-3：30

Abstract ：The study of stationary Schrodinger equations has a long history. Even for the case that the Schrodinger operator is indefinite, many interesting results has been obtained by linking theorems.

In recent years, more general Schrodinger type equations such as Schrodinger-Poisson systems, quasilinear Schrodinger equations, have captured great interest. Most study focus on the case that the Schrodinger operator is definite so that the zero function is a local minimizer of the energy functional. We discovered that for such equations, unlike the classical Schrodinger equations mentioned above, when the Schrodinger operator is indefinite, the linking theorems is not applicable.

Fortunately, we found that the local linking theory of Shujie Li and Jiaquan Liu is quite suitable for treating this kind of problems. In this talk, we will demostrate how local linking could be applied to indefinite Schrodinger-Poisson systems, quasilinear Schrodinger equations, and fourth order elliptic equations with the Laplacian of u^2.

报告人简介：刘轼波, 男, 1975年生于广东. 在兰州大学获得学士和硕士学位后, 到中国科学院数学所学习, 于2003年获得博士学位. 2005年从北京大学数学研究所博士后出站, 到厦门大学任副教授. 2008年任汕头大学教授, 2011年任厦门大学教授. 现为厦门大学数学系教授、博士生导师. 先后主持国家自然科学基金青年项目和面上项目, 以及福建省杰出青年基金项目. 2013年入选意大利国际理论物理中心(ICTP)协联成员, 2017年受国家留学基金委资助到美国圣母大学访问一年. 他的研究领域是非线性泛函分析、非线性偏微分方程的变分方法.

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