Convergence and Divergence of the Solutions of a Neutral Difference Equation

Abstract EN

We investigate the asymptotic behavior of the solutions of a neutral type difference equation of the form Δ[x(n)+cx(τ(n))]+p(n)x(σ(n))=0, where τ(n) is a general retarded argument, σ(n) is a general deviated argument (retarded or advanced), c∈ℝ, (p(n))n≥0 is a sequence of positive real numbers such that p(n)≥p, p∈ℝ+, and Δ denotes the forward difference operator Δx(n)=x(n+1)−x(n).

Also, we examine the asymptotic behavior of the solutions in case they are continuous and differentiable with respect to c.