Abstract：
The study of stationary Schrodinger equations has a long history. Even for the case that the Schrodinger operator is indefinite, many interesting results have 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. Almost all 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 demonstrate 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.
Biography:
After obtaining his BSc and MSc from Lanzhou University in 1997 and 2000 respectively, he went to the Institute of Mathematics of CAS for further study and got his Ph.D. degree in mathematics in 2003. Then he was a postdoc at Peking University for two years. In 2005, he joined Xiamen University as an associate professor. He moved to Shantou University and was appointed as professor in 2008. He returned to Xiamen University as professor in 2011. He was a regular associate of ICTP for the period 2014—2019.
Seminar by the NYU-ECNU Institute of Mathematical Sciences at NYU Shanghai