Existence of solutions for second order impulsive control problems with boundary conditions

Control of impulsive differential equations appear naturally in physical phenomena. Most often these phenomena take place during a finite time interval. This leads to the study of boundary value problems for control of impulsive differential equations. In this paper we address the problem of existence of solutions of control of impulsive differential equations of second order subjected to two-point boundary conditions. Our approach is based on the Granas topological transversality theorem and the Schauder fixed point theorem. The uniqueness of solutions is also discussed.