Controllability Of Second Order Impulsive Systems With Infinite Delay In Banach Spaces

This paper studies the existence of the mild solutions and the controllability ofsecond order impulsive functional differential systems with infinite delay in Banachspaces. Sufficient conditions are formulated and proved for the controllability of thesystem. We establish the results by using Krasnoselskii’s fixed point theorem andcontraction mapping theorem, combining with the properties of cosine and sinefamilies of operators.Respectively, we study two conditions: one is with compactnesscondition on the sine family of operators；the other is with non-compactness conditionon the sine family of operators. Fanally, we verify the conclusion by an example.