Convergence and Divergence of the Solutions of a Neutral Difference Equation

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...

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Bibliographic Details
Published in:Journal of Applied Mathematics 2011-01, Vol.2011 (2011), p.434-451-027
Main Authors: Chatzarakis, G. E., Miliaras, G. N.
Format: Article
Language:English
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Summary: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.
ISSN:1110-757X
1687-0042
DOI:10.1155/2011/262316