2017
Том 69
№ 6

All Issues

Asymptotic behavior of higher-order neutral difference equations with general arguments

Chatzarakis G. E., Khatibzadeh H., Miliaras G. N., Stavroulakis I. P.

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Abstract

We study the asymptotic behavior of solutions of the higher-order neutral difference equation $$Δm[x(n)+cx(τ(n))]+p(n)x(σ(n))=0,N∍m≥2,n≥0,$$ where $τ (n)$ is a general retarded argument, $σ(n)$ is a general deviated argument, $c ∈ R; (p(n)) n ≥ 0$ is a sequence of real numbers, $∆$ denotes the forward difference operator $∆x(n) = x(n+1) - x(n)$; and $∆^j$ denotes the jth forward difference operator $∆^j (x(n) = ∆ (∆^{j-1}(x(n)))$ for $j = 2, 3,…,m$. Examples illustrating the results are also given.

English version (Springer): Ukrainian Mathematical Journal 65 (2013), no. 3, pp 478-499.

Citation Example: Chatzarakis G. E., Khatibzadeh H., Miliaras G. N., Stavroulakis I. P. Asymptotic behavior of higher-order neutral difference equations with general arguments // Ukr. Mat. Zh. - 2013. - 65, № 3. - pp. 430-450.

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