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中立型脉冲发展方程解的存在性和唯一性
汪小梅¹, 张志强², 朱华³
1.军事经济学院基础部数理教研室, 湖北武汉 430035;2.武昌工学院信息工程学院, 湖北武汉 430065;3.湖北大学知行学院计科系数学教研室, 湖北武汉 430010

摘要:

本文研究了一类非线性中立型脉冲发展方程解的存在性和唯一性的问题.利用迭代分析方法结合半群理论的知识,得到了其解的表达式,并构造解的迭代序列,同时证明了其解的存在性和唯一性.通过研究发现其解的存在性和唯一性与脉冲时滞条件密不可分,利用迭代分析法求解此类问题具有一定的优越性.

关键词: 脉冲迭代存在唯一

DOI：

分类号:O175.29

基金项目:

THE EXISTENCE AND UNIQUENESS OF THE SOLUTION FOR NEUTRAL IMPULSIVE EVOLUTION EQUATIONS

WANG Xiao-mei¹, ZHANG Zhi-qiang², ZHU Hua³

1.Department of Mathematics and Physics, Military Economics Academy, Wuhan 430035, China;2.College of Information Engineering, Wuchang Institute of Technology, Wuhan 430065, China;3.Department of Basic Sciences, Zhixing College, HuBei University, Wuhan 430010, China

Abstract:

In this paper, the existence and uniqueness of solutions are obtained. By studying the structure of iterative sequence of solutions to a class of nonlinear impulsive evolution equations with iterative analysis method and semigroup theorem, we show that the existence and uniqueness of solutions are inseparable linked with impulsive delay condition. It has certain superiority to solve such problems with iterative analysis.

Key words: impulsive iterative existence uniqueness