Oscillation Criteria for the Solutions of Higher Order Functional Dierence Equations of Neutral type

Abstract

In this paper, necessary and sufficient conditions are obtained so that the neutral functional difference equation $$\Delta^{m}\big(y_n-y_{\tau(n)}\big) + q_nG(y_{\sigma(n)})=f_n,\quad n\geq n_0,$$ admits a positive bounded solution, where $$m \geq 1$$ is an odd integer, $$\Delta$$ is the forward difference operator given by $$\Delta y_n = y_{n+1}-y_n$$; $$\{f_n\}$$, $$\{q_n\}$$, are sequences of real numbers with $$q_n \geq 0$$, $$G \in C(\mathbb{R},\mathbb{R}).$$ The results of this paper improve and extend some recent work [6,15].