局部条件下的二阶哈密顿系统同宿轨的存在性与多重性

Hamiltonian system is a classic and modern reserach field, covering widely in subjects such as mathematical and physical science, bioscience and social science. It is applied to studying the influence of local growth conditions and non-coercive conditions with variational methods to the existence and multiplicity of homoclinic orbits for the second order Hamiltonian systems , which there is few scholar studying. This project will promote the further research and consideration of this issue and provide the theoretical basis for the research of those issues related to other subjects.

哈密顿系统理论是既经典又现代的研究领域，它广泛存在于数理科学，生命科学，社会科学等学科领域中。本项目致力于研究局部增长条件结合非强制条件对二阶哈密顿系统同宿轨的存在性与多重性的影响。到目前为止，较少有学者研究该条件下二阶哈密顿系统同宿轨的存在性与多重性问题。本项目将促进对该类问题的进一步研究和关注，为其他学科的相关问题研究提供理论基础。

在位势函数满足局部增长的条件下,本项目利用变分方法研究了二阶哈密顿系统同宿轨解的存在性与多重性问题..到目前为止，此类问题的研究成果还较少,因此本项目的结论填补了对此类问题研究的空白,同时也为其他学科的相关问题研究提供理论基础.