Asymptotic behavior of higher-order neutral difference equations with general arguments
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 forwa...
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| Datum: | 2013 |
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| Hauptverfasser: | , , , , , , , |
| Format: | Artikel |
| Sprache: | Englisch |
| Veröffentlicht: |
Institute of Mathematics, NAS of Ukraine
2013
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| Online Zugang: | https://umj.imath.kiev.ua/index.php/umj/article/view/2429 |
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| Назва журналу: | Ukrains’kyi Matematychnyi Zhurnal |
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Ukrains’kyi Matematychnyi Zhurnal| Zusammenfassung: | 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. |
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