【作者】 李蕾；

【导师】 宋叔尼；

【作者基本信息】 东北大学 ， 基础数学， 2012， 硕士

【摘要】 脉冲微分方程是微分方程的一个重要分支,它不仅反映了一种瞬间突变现象即脉冲现象,而且能考虑到这种现象对状态的影响,在众多科学领域中有着很好的应用.近年来,脉冲微分方程得到了广泛重视和深入发展,其理论比不含脉冲的微分方程更丰富,而且能更真实地反映客观世界的现象,因而更具有研究价值.随着脉冲微分方程理论的发展,人们开始关注脉冲微分方程理论的研究.本文将运用不动点理论研究下面具有四点边值条件的脉冲微分方程解的存在性.又因为多点边值问题具有广泛的应用背景,具有很重要的研究价值,我们又运用该不动点定理讨论了p+2点边值条件的脉冲微分方程解的存在性.更多还原

【Abstract】 Impulsive differential equation is an important branch of differential equations. It not only reflects a kind of instantaneous perturbation phenomenon namely impulsive phenomenon, but also considers the influence of this kind of phenomenon to the appearance. It has been well used in many scientific fields and has been drawed attention to extensively and developed deeply in recent years. It is more abundant than the other equations and it could more truly reflect the phenomenon in the objective world, so it is more worth studying. Multi-point boundary value problem for impulsive differential equations is paid attention by people to study the development of the theory for impulsive differential equations.The fixed point theorem is used to study the existence of solutions for the following impulsive differential equations of four-point boundary value problemsAs Multi-point boundary value problem have widely applied background, they have important value. The fixed point theorem is used to study the existence of solutions for the following impulsive differential equations of p+2-point boundary value problem:更多还原