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

Advances in Difference Equations

Gang Li¹  Shaochun Ji² 

[1] Faculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, P.R. China;School of Mathematical Science, Yangzhou University, Yangzhou, P.R. China

关键词: impulsive conditions;    nonlocal conditions;    Hausdorff measure of noncompactness;    fixed point theorem;   

DOI  :  10.1186/1687-1847-2012-182

学科分类：数学（综合）

来源: SpringerOpen

【 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.

【 授权许可】

CC BY