On the behavior of solutions of neutral impulsive difference equations of second order

The work embodied in this paper is the study of oscillation properties of a class of second order neutral impulsive difference equations with constant coefficients of the form: {Delta(2)[u(n) - pu(n - alpha)] + qu(n - beta) = 0, n not equal m(j) (Delta) under bar[Delta(u(m(j) - 1) - pu(m(j) - alpha - 1))] + ru(m(j) - beta - 1) = 0, j is an element of N for p is an element of R. In addition, an effort has been made here to apply the constant coefficient results to nonlinear impulsive difference equations with variable coefficients of the form: {Delta(2)[u(n) - p(n)f(u(n - alpha))] + q(n)h(u(n - beta)) = 0, n not equal m(j) (Delta) under bar[Delta(u(m(j) - 1) - p(m(j) - 1)f(u(m(j) - alpha - 1)))] + r(m(j) - 1)h(u(m(j) - beta - 1)) = 0, j is an element of N for p(n) >= 1. Our method suggests the explicit structure of the solution of impulsive difference equations.