四川师范大学学报（自然科学版）2012，Vol.35Issue(6)：802-808,7.DOI:10.3969/j.issn.1001-8395.2012.06.018
Banach空间中一阶脉冲微分方程组的无穷边值问题解的存在唯一性
The Existence and Uniqueness of Solutions of Infinite Boundary Value Problems for First-order Impulsive Differential Systems in a Banach Space
摘要
Abstract
In this paper, the existence and uniqueness of solutions for the following nonlinear first-order impulsive differential systems with infinite boundary value problems are considered u'=f(t,u(t),v(t)),v'=g(t,u(t),v(t)),VtEj,t=tk,u/t=tk=1k(U(tk),v(tk)),v/t=tk=jk(u(tk),v(tk)),k=1.2.`````u(oo)=Bu(0),v(oo)=8v(0). Firstly, the existence of solution for the problem is established based on the H. Monch' s fixed point theorem and the measures of non-compactness. Furthermore, based on the existence of solution, the uniqueness of solution is proved by using the argument of contradiction. The obtained results in this paper are new and extend some known results. Finally, an example is presented to illustrate the effects of the present theorems.关键词
Banach空间/H.M(o)nch不动点定理/一阶脉冲微分方程组/无穷边值问题/存在性和唯一性Key words
Banach space/ H. MBnch's fixed point theorem/ first-order impulsive differential systems/ infinite boundary value problems/ existence and uniqueness分类
数理科学引用本文复制引用
汤小松,王志伟,罗节英..Banach空间中一阶脉冲微分方程组的无穷边值问题解的存在唯一性[J].四川师范大学学报（自然科学版）,2012,35(6):802-808,7.基金项目
江西省自然科学青年基金(20114BAB211015)资助项目 （20114BAB211015）
