Oscillatory property of higher order nonlinear difference equations

Abstract

In this paper, we study the oscillatory and asymptotic behaviour of solutions of higher order nonlinear difference equations of the form Δ r n (Δ d − 1 x n ) δ + F(n,ϰ n ) = 0. We obtain some necessary and sufficient conditions for all bounded solutions of (∗) to be oscillatory and for (∗) to have a nonoscillatory solution of a special form.