Controllability of Second-Order Systems with Nonlocal Conditions in Banach Spaces

Abstract

In this article, exact controllability of second-order semilinear differential system with nonlocal conditions in Banach spaces is studied. To establish sufficient conditions for exact controllability, Sadovskii's fixed point theorem together with the theory of strongly continuous cosine family is been used. The cosine family and the nonlinear function associated with the system are assumed to be non-compact. An example is given to illustrate the developed theory.