In this paper, first order impulsive difference equations with linear boundary conditions are discussed. By using a new comparison theorem and the method of upper and lower solutions coupled with the monotone iterative technique, criteria on the existence of minimal and maximal solutions are obtained. AMS subject classification: 34D20, 34A37.

Sufficient conditions are given for the solvability of boundary value problems on an infinite interval for nonlinear two dimensional generalized and impulsive differential systems.