节点文献
泛函方法在积—微分方程中的应用
The Application of Functional Theory in Integro-Differential Equations
【作者】 郑建；
【导师】 宋光兴；
【作者基本信息】 中国石油大学 ， 应用数学， 2008， 硕士
【摘要】 本文对实Banach空间中二阶混合型积-微分方程进行了研究，主要分为以下三个方面：二阶混合型积-微分方程的初值问题，二阶混合型积-微分方程的两点边值问题及二阶混合型积-微分方程的周期边值问题．在对上述问题的研究过程中均采用了上下解方法和单调迭代方法，证明了相应问题最大解和最小解的存在性，并且得到了逼近解的单调迭代序列.在本文中建立了全新的比较定理，并且方程的形式也更加也丰富，扩大了方程的适用范围，推广了原有文献中的一些结果.本文共分五章.第一章为前言.第二章、第三章分别讨论了二阶混合型积-微分方程的初值问题和两点边值问题.第四章研究了二阶混合型积-微分方程的周期边值问题，其中又分为不含微分项u和含有微分项u的周期边值问题.最后对本文全面总结.
【Abstract】 In this thesis, we investigate the second order integro-differential equations. The main research includes three aspects: the initial value problem (IVP), the two-point boundary value problem (BVP) and the periodic boundary value problem (PBVP).By using the upper and lower solutions method and monotone iterative technique, we obtain the existence of the maximal and minimal solutions and the iterative sequence of corresponding solutions for the Integro-differential equations. In this thesis, we establish new comparison results and the results obtained generalize and improve the results corresponding to those obtained by others.The thesis is divided into five chapters according to contents. The first chapter is a preface. In the second and the third chapter, the IVP and BVP for second-order integro-differential equations are investigated. In the fourth chapter, we investigate the PBVP for second-order integro-differential equations and this problem includes two aspects: without u′item and with u′item. The last chapter is the summary of this thesis.