Banach空间中一阶周期边值问题的弱解  

The Generalized Solutions of First Order Periodic Boundary Value Problems in Banach Spaces

作　　者：伊继金[1] 

机构地区：[1]南开大学数学科学学院,天津300071

出　　处：《工程数学学报》2007年第6期1070-1074,共5页Chinese Journal of Engineering Mathematics

基　　金：国家自然科学基金(10571090).

摘　　要：本文研究了Banach空间中具有Carathéodory函数的非线性Volterra型积分微分方程。对于这一类积分微分方程,我们试图证明它在Banach空间中解的存在性。为此,我们加入一些必要的限制条件,然后利用上、下解方法和单调迭代法得到解序列,解序列的极限即为非线性Volterra型积分微分方程的解。In this paper, we study the nonlinear integro-differential equations of Volterra type with Carathéodory functions in Banach spaces. For this kind of integro-differential equations, we prove the existence of the solutions in Banach spaces and present some necessary conditions. By using the method of lower- upper solutions and monotone iteration, we get sequence of solutions, whose limits are the solutions of equations of Volterra type.

关 键 词：单调迭代 半序 上下解 正规锥 

分 类 号：O177[理学—数学]