Global solutions for second order impulsive integro-differential equations in Banach spaces

This paper regards initial value problem for second order impulsive integro-differential equations as some nonlinear vector system. By means of the Mönch′s fixed point theorem, some existence theorems of solutions of the initial value problem are established. The results are newer than all of the previous ones because of the more general form compactness-type condition and the weaker restriction of its coefficients. An example is given to demonstrate our results. Annotation shows that our method can be used to solve the impulsive boundary value problems. Key–Words: Impulsive integro-differential equations, initial value problem, Boundary value problem, Compactness-type condition, Banach space, Fixed point, Operator norm of the matrix.