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中科院数学与系统科学研究院

数学研究所

 

非线性分析研讨班

 

报告人刘轼波 教授厦门大学

 Local linking and indefinite Schrdinger equations

  2019.04.29(星期一),11:00-12:00

  点:数学院南楼N820

  要:The study of stationary Schrdinger equations has a long history. Even for the case that the Schrdinger operator is indefinite, many interesting results has been obtained by linking theorems. In recent years, more general Schrodinger type equations such as Schrdinger-Poisson systems, quasilinear Schrdinger equations, have captured great interest. Most study focus on the case that the Schrdinger 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 Schrdinger 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 Schrdinger-Poisson systems, quasilinear Schrdinger equations, and fourth order elliptic equations with the Laplacian of u^2.

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