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.
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页数：14
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