Hamilton系统基态解的存在性及稳定性

Hamiltonian system is widely used in the mathematical science, life science and various fields of social science. The periodic solutions, homoclinic orbits and stability of the Hamiltonian systems have abroad applied background and profound theoretical significance. Based on the existing literature, the project will apply variational methods and the critical point theory to develop and expand the theoretical and practical research on the continuous(discrete) Hamiltonian system from the following aspects: the existence of the ground state periodic solutions and ground state homoclinic solutions of Nehari type or Nehari-Pankov type, the existence and nonexistence of the nontrivial homoclinic orbits, the boundedness and stability of the solutions. By deepening the mathematical tools, we will explore new methods and techniques to obtain a number of new and essential results, and promote the development of the qualitative theory of Hamiltonian system.

Hamilton系统广泛存在于数理科学、生命科学及社会科学的各个领域。Hamilton系统周期解、同宿轨存在性和稳定性有着广泛的应用背景和重要的理论意义。本项目将借助变分方法与临界点理论，在已有文献的基础上，发展和开拓连续（离散）Hamilton系统Nehari型或Nehari-Pankov型周期基态解、同宿基态解的存在性、非平凡同宿轨的存在性、不存在性、Hamilton系统解的有界性、稳定性的理论及应用研究，深化数学工具，探讨新的方法、新的技巧，对所研究的问题获得若干全新的、本质性的结果，推进Hamilton系统定性理论的发展。

Hamilton系统广泛存在于数理科学、生命科学及社会科学的各个领域。Hamilton系统周期解、同宿轨存在性和稳定性有着广泛的应用背景和重要的理论意义。本项目借助于变分方法与临界点理论，在已有文献的基础上，建立了连续（离散）Hamilton系统Nehari型或Nehari-Pankov型周期基态解、同宿基态解的存在性、非平凡同宿轨的存在性、不存在性、Hamilton系统解的有界性若干全新的、本质性的结果，并发展和开拓了新的方法和新的技巧。