一类算子方程解的存在性.docVIP

一类算子方程解的存在性 熊春连1，段华贵2 1 天津城市建设学院基础教学部，天津 300384 2 南开大学数学科学学院，天津　 300071 摘要：在本文中，我们利用迭代方法和偏序理论研究了完备度量空间与 Banach 空间中一类方 程 Lx=N(x,y) 的解和耦合解的存在性。作为应用，我们讨论了一类积分 -微分方程的两点边值 问题。 关键词：偏序，Banach 空间, 正规锥, 积分 -微分方程, 耦合解. 中图分类号： O177.91 The existence of solutions of a class of operator equations Chunlian XIONG1, Huagui DUAN2 1 Department of Fundamental, Tianjin Institute of Urban Construction, Tianjin 300384 2 School of Mathematical Sciences and LPMC, Nankai University, Tianjin 300071 Abstract: In this paper, iterative techniques and the partial order theory are used to study the existence of coupled solutions and solutions for an operator equation Lx=N(x,y) in a complete metric space and Banach space, respectively. And then main results are applied to two point boundary value problems of an integro-di?erential equation. Key words: partially order, Banach space, normal cone, integro-di?erential equation, coupled solutions. 0 Preliminaries Iterative techniques (cf. [1], [2], [3], [4] and [5]) and partial order theory (cf. [6], [7], [8] and [9]) play an important role in studying nonlinear problems. Nieto [5] has studied the operator equation x = Nx by virtue of monotone iterative techniques. Feng and Liu [6] has proved the existence of solutions for general operator equation Lx = Nx by using partial order methods. In this paper, we continue to investigate more general operator equation Lx = N(x, y)  (0.1) 基金项目： Partially supported by SRFDP (200800551002) and NNSFC . 作者简介： Xiong Chunlian（1976-），female，major research direction：?nancial engineering. Correspondence author： Duan Huagui（1977-），male，associate professor，major research direction：nonlinear analysis. -1- in complete metric spaces and Banach spaces, and we obtain the existence theorems of coupled solutions and solutions of (0.1). And then the main results are applied to two point bound- ary value problems of an integro-di?erential equation. In fact, many di?erential and integral equations can be chan