Convergence and Divergence of the Solutions of a Neutral Difference Equation

G. E. Chatzarakis and G. N. Miliaras

Journal of Applied Mathematics, 2011, vol. 2011, issue 1

Abstract: 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.

Date: 2011
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https://doi.org/10.1155/2011/262316

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnljam:v:2011:y:2011:i:1:n:262316

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