A unified approach to nonlocal impulsive differential equations with the measure of noncompactness

被引：13

作者：

Ji, Shaochun ^{[1
,2
]}

Li, Gang ^{[1
]}

机构：

[1] Yangzhou Univ, Sch Math Sci, Yangzhou 225002, Peoples R China

[2] Huaiyin Inst Technol, Fac Math & Phys, Huaian 223003, Peoples R China

来源：

ADVANCES IN DIFFERENCE EQUATIONS | 2012年

基金：

中国国家自然科学基金;

关键词：

impulsive conditions; nonlocal conditions; Hausdorff measure of noncompactness; fixed point theorem; BANACH-SPACES; EVOLUTION-EQUATIONS; INTEGRAL-EQUATIONS; EXISTENCE; INCLUSIONS; CONTROLLABILITY; THEOREMS;

D O I：

10.1186/1687-1847-2012-182

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

This paper is concerned with the existence of mild solutions to impulsive differential equations with nonlocal conditions. We firstly establish a property of the measure of noncompactness in the space of piecewise continuous functions. Then, by applying this property and Darbo-Sadovskii's fixed point theorem, we get the existence results of impulsive differential equations in a unified way under compactness conditions, Lipschitz conditions and mixed-type conditions, respectively. MSC: 34K30, 34G20.

引用

页数：14