Monotone iterative technique for the initial value problem for differential equations with non-instantaneous impulses

Abstract

An algorithm for constructing two monotone sequences of upper and lower solutions of the initial value problem for a scalar nonnlinear differential equation with non-instantaneous impulses is given. The impulses start abruptly at some points and their action continue on given finite intervals. We prove that the functional sequences are convergent and their limits are minimal and maximal solutions of the considered problem. An example is given to illustrate the results.