Oscillation Criteria for the Solutions of Higher Order Functional Dierence Equations of Neutral type
Radhanath Rath *
P.G Department of Mathematics, Khallikote Autonomous College, Berhampur, Odisha, India, 760001.
Ajit kumar Bhuyan
Department of Mathematics., G.E.C, Bhubaneswar,Odisha, India.
B.L.S. Barik
Department of Mathematics, K.I.S.T, Bhubaneswar,Odisha, India.
*Author to whom correspondence should be addressed.
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].
Keywords: Asymptotic behavior, dierence equation, oscillatory solution, non oscillatory solution