从生物数学模型中的到的奇异扰动Schrodinger方程的凝聚现象以及解的存在唯一性问题等一直是数学研究的热门问题。这本项目中，我们将利用Lypunov-Schmidt约化的方法来研究Schrodinger方程在有界区域的边界凝聚现象，以及其在全空间中的存在唯一性问题。同时我们将考虑与之相关的Lane-Emden方程的弱解的存在性及正则性问题。

Singularly perturbation problem arsing from the mathematical biology has been studied by mathematicians over the last 30 years. In this project, we will study the boundary concentration phenomena for the singularly perturbation problem in bounded domain. We are also interested in the existence and uniqueness problem for the Schrodinger equation in R^n. The existence of weak solution and regularity problem of the related Lane-Emden equation will also been studied. The basic tool we will use is the Lyapunov-Schmidt reduction method.