Controllability of nonlinear impulsive second order integrodifferential evolution systems in Banach spaces

Abstract

This paper deals with the controllability of impulsive second order integrodifferential systems in Banach spaces. Sufficient conditions for the controllability are derived with the help of the fixed point theorem due to Sadovskii and the theory of strongly continuous cosine family of operators. An example is provided to show the effectiveness of the proposed results. Further, we study the controllability of second order integrodifferential evolution systems with impulses by using the Schaefer fixed-point theorem.