| Banach空间中二阶非线性脉冲微分方程初值问题解的存在性 |
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| 引用本文： | 张海燕.Banach空间中二阶非线性脉冲微分方程初值问题解的存在性[J].安庆师范学院学报(自然科学版),2015(3). |
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| 作者姓名： | 张海燕 |
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| 作者单位： | 宿州学院 数学与统计学院,安徽 宿州,234000 |
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| 基金项目： | 安徽省教育厅自然科学基金重点项目 |
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| 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。
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| 关 键 词： | 脉冲微分方程 初值问题 不动点定理 非紧性测度 |
Existence of Solutions for a Class Initial Value Problems of Second-Order Nonlinear Impulsive Differential Equations in Banach Spaces |
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| Abstract: | 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-sults are extended and improved. |
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| Keywords: | impulsive differential equations initial value problems fixed point theorem measure of noncompactness |
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