Local linking and indefinite Schrodinger equations
非线性分析专题报告
报告题目(Title)：Local linking and indefinite Schrodinger equations
报告人(Speaker)：刘轼波教授 （厦门大学数学科学学院）
地点(Place)：电子楼101
时间(Time)：4月25日 8:00-9:00
邀请人(Inviter)：唐仲伟
报告摘要
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.
