本项目拟发展临界点理论的新方法，应用于无穷维哈密顿力学中出现的微分方程问题。项目将建立抽象理论并关注于研究Dirac方程、反应-扩散系统以及椭圆系统等具有强不定结构的非线性微分方程在参数影响下的渐近行为。..本项目致力于给出含参数的强不定问题在一般型非线性条件下解的存在与集中现象的分析刻画。特别地，本项目拟关注于强不定问题在参数、位势函数的局部几何以及非线性部分共同作用下其束缚态解的存在与渐近行为。本项目拟在理论与应用两个方面对强不定问题作出深入研究。

This project is aimed at to develop new methods in Critical Point Theory oriented towards differential equations in infinite-dimensional Hamiltonian mechanics. Theoretical results are motivated by and in turn applied to the parameter-effect on the nonlinear differential equations as Dirac equation, Reaction-Diffusion systems and Elliptic systems...Purpose of this project is to study some analytical characterization for the existence and concentrating phenomenon for strongly indefinite problems involving some general nonlinearities. Specifically, we will focus on the existence and asymptotic behavior of some bound-state solutions under the interaction of the varying parameters, the local geometry of the potential functions and the nonlinear terms. We expect to make some substantial contributions to both aspects of basic theory and applications.