Banach空间中二阶非线性脉冲微分方程初值问题解的存在性  

Existence of Solutions for a Class Initial Value Problems of Second- Order Nonlinear Impulsive Differential Equations in Banach Spaces

作　　者：张海燕[1] 

机构地区：[1]宿州学院数学与统计学院,安徽宿州234000

出　　处：《安庆师范学院学报（自然科学版）》2015年第3期19-21,34,共4页Journal of Anqing Teachers College(Natural Science Edition)

基　　金：安徽省教育厅自然科学基金重点项目(KJ2014A252)

摘　　要：利用Monch不动点定理和分段估计方法,结合Gronwall不等式,研究了Banach空间中一类二阶非线性脉冲微分方程初值问题解的存在性。将该问题转化为等价的一阶非线性脉冲积分方程,在较弱的非紧性条件和先验估计条件下,获得了其解的存在性充分条件,改进和推广了相关文献的结果。By using the Monch fixed theorem and a piece wise estimation method, and combining with a Gronwall inequality, a class initial value problems of second -order nonlinear impulsive differential equations in Banach Spaces is investigated, which can be reduced to the equivalent first - order nonlinear impulsive integral equation. Under weaker noncompactness and priori esti- mate conditions, some sufficient results on the existence of solution for the initial value problem are established. Some known re- suhs are extended and improved.

关 键 词：脉冲微分方程 初值问题 不动点定理 非紧性测度 

分 类 号：O175.8[理学—数学]