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

作者：Ji, Shaochun^*; Li, Gang

来源：Advances in Difference Equations, 2012, 2012(1): 182.

DOI：10.1186/1687-1847-2012-182

• impulsive conditions
• nonlocal conditions
• Hausdorff measure of noncompactness
• fixed point theorem

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.

• 出版日期2012
• 单位淮阴工学院; 扬州大学