Oscillation of higher order neutral functional difference equations with positive and negative coefficients

Mathematica Slovaca

R. Rath¹  S. Rath¹  B. Barik¹ 

关键词: oscillatory solution;    nonoscillatory solution;    asymptotic behaviour;    difference equation;   

DOI  :  10.2478/s12175-010-0018-6

学科分类：数学（综合）

来源: Slovenska Akademia Vied * Matematicky Ustav / Slovak Academy of Sciences, Mathematical Institute

【 摘 要 】

Sufficient conditions are obtained so that every solution of the neutral functional difference equation $$Delta ^m (y_n - p_n y_{au (n)} ) + q_n G(y_{sigma (n)} ) - u_n H(y_{alpha (n)} ) = f_n ,$$ oscillates or tends to zero or ±∞ as n → ∞, where Δ is the forward difference operator given by Δx n = x n+1 − x n, p n, q n, u n, f n are infinite sequences of real numbers with q n > 0, u n ≥ 0, G,H ∈ C(ℝ,ℝ) and m ≥ 2 is any positive integer. Various ranges of {p n} are considered. The results hold for G(u) ≡ u, and f n ≡ 0. This paper corrects, improves and generalizes some recent results.

【 授权许可】

Unknown