Controllability of nonlocal impulsive differential equations with measure of noncompactness

Abstract

\begin{abstract}
This paper is concerned with the controllability of impulsive differential equations with nonlocal conditions. First, we establish a property of measure of noncompactness in the space of piecewise continuous functions. Then, by using this property and Darbo-Sadovskii's Fixed Point Theorem, we get the controllability of nonlocal impulsive differetial equations under compactness conditions, Lipschitz conditions and mixed-type conditions respectively.\\
{\bf keywords}: Controllability, impulsive differential equations, nonlocal conditions, measure of non compactness, fixed point theorem.
\end{abstract}