Asymptotic behavior in neutral difference equations with negative coefficients and several delay arguments

Abstract

In this paper, we study the asymptotic behavior of the solutions of a neutral type difference equation of the form

Δ[x(n)+∑_{j=1}^{w}q_{j}(n)x(τ_{j}(n))]-p(n)x(σ(n))=0,    n≥0

where (-p(n))_{n≥0} is a sequence of negative real numbers such that p(n)≥p, p∈ℝ₊, τ_{j}(n), j=1,...,w are general retarded arguments, σ(n) is a general deviated argument, (q_{j}(n))_{n≥0}, j=1,...,w are sequences of real numbers, and Δ denotes the forward difference operator Δx(n)=x(n+1)-x(n).