项目名称: 脉冲微分方程与包含的同宿、异宿轨及相关问题研究
项目编号: No.11261020
项目类型: 地区科学基金项目
立项/批准年度: 2013
项目学科: 数理科学和化学
项目作者: 何小飞
作者单位: 吉首大学
项目金额: 45万元
中文摘要: 研究微分方程特殊解(如周期解、同宿轨和异宿轨) 的存在性及这些解的动力学行为是微分方程定性理论中非常重要的一个方面。 本课题运用非线性分析中变分方法和临界点理论及非光滑分析研究脉冲微分方程及微分包含问题各类解的存在性、多解性及解的估计。重点研究由脉冲效应引起的周期解、同宿解及异宿解;进一步,将系统地建立脉冲微分包含的变分框架,应用和发展非光滑临界点理论,建立脉冲微分包含的临界点存在性定理和多解性定理,给出新的结论,使之便于使用。本课题的的完成将对脉冲微分方程及微分包含的理论起到促进作用,同时也将扩展变分方法和临界点理论的应用范围。
中文关键词: 脉冲;微分方程;微分包含;临界点理论;Hamilton系统
英文摘要: It is of great significance to the qualitative theory of differential equations to study the existence of special solutions of differential equations and their dynamical behaviors, such as periodic solutions, homoclinic solutions and heteroclinic solutions. Based on the variational method, critical point theory and nonsmooth analysis, we investigate the existence, the mulpliticity and the estimation of solutions for impulsive differential equations and differential inclusions. We mainly concerns the periodic solutions, homoclinic solutions and heteroclinic solutions caused by impulsive effects. By systematically establishing the variational framework for impulsive differential inclusions, we will apply and develop nonsmooth critical point theory to establish the criterion for the existence of critical points. Some new results will be obtained so that it will be a useful applications. After the completion of this study, it will promote the theory of impulsive differential equations and differential inclusions, and therefore extend the applications of variational method and critical point theory.
英文关键词: Impulse;Differential Equation;Differential Inclusions;Critical Point Theory;Hamiltom system