带变号位势的Hamilton系统的同宿轨

项目名称： 带变号位势的Hamilton系统的同宿轨

项目编号： No.11426184

项目类型： 专项基金项目

立项/批准年度： 2015

项目学科： 数理科学和化学

项目作者： 吕颖

作者单位： 西南大学

项目金额： 3万元

中文摘要： 本项目拟运用变分方法研究带变号位势的Hamilton系统同宿轨的存在性与多解性。Hamilton系统的同宿轨具有非常重要的数学物理意义，也是非线性分析研究领域十分关注的问题。近二十年，众多国内外学者运用非线性泛函分析方法研究其存在性与多重性，已取得了丰富而深刻的结果，但现有结果较少涉及带变号位势的情形，尤其在本项目将要讨论的几类条件下的结果几乎没有。本项目将通过分析具体问题总结这类问题的本质困难，探寻解决问题的新思路，旨在促进对这类问题的进一步关注和研究，同时加深人们对数学物理中的这类重要模型的认识和理解。

中文关键词： Hamilton系统；同宿轨；变号位势；局部超二次；渐近二次

英文摘要： In this project we will use variational methods to investigate the existence and multiplicity of homoclinic orbits for Hamiltonian systems with sign-changing potentials. Homoclinic orbits of Hamiltonian systems is very important in Mathematical physics, also is a problem of great concern in nonlinear analysis fields. In recent two decades, many domestic and foreign scholars have used nonlinear functional analysis methods to study the existence and multiplicity of homoclinic orbits for Hamiltonian systems, and obtained rich and deep results, but less results consider the Hamiltonian systems with sign-changing potentials, especially under the conditions which will be discussed in this project. In this project we will summarize intrinsic difficultiy for these problems and find new ideas in study of these problems, aim to promote the further research on these problems, and at the same time enhance people's understanding and in-depth knowledge of these important models in Mathematical physics.

英文关键词： Hamiltonian systems；Homoclinic orbit；sign-changing potential；Local superquadratic；Asymptotically quadratic