Mathematical Sciences: Critical Point Theory and Applications

该项目将涉及各种变分的研究 动力系统和偏微分方程中的问题。 研究的基本问题包括（a）三体和n体型 问题，（B）温斯坦猜想，它涉及周期性 奇维紧致流形上的轨道，（c） 超线性椭圆问题的解，以及（d）椭圆 涉及临界Sobolev指数的变分问题， 包括可收缩域和曲率问题 问题 除了在部分领域作出贡献外， 微分方程和微分几何，这项工作可以 应用于动力系统和势理论。

This project will involve the study of various variational problems in dynamical systems and partial differential equations. The basic problems studied include (a) three and n-body type problems, (b) the Weinstein conjecture, which concerns periodic orbits on odd-dimensional compact manifolds, (c) the existence of solutions to superlinear elliptic problems, and (d) elliptic variational problems involving the critical Sobolev exponent, including problems on contractible domains and curvature problems. In addition to making contributions in the areas of partial differential equations and differential geometry, this work can be applied to dynamical systems and potential theory.