Asymptotic properties of solutions to difference equations of Emden-Fowler type
We study the higher order difference equations of the following form mxn = an f(xσ(n) ) + bn. We are interested in the asymptotic behavior of solutions x of the above equation. Assuming f is a power type function and ∆ myn = bn, we present sufficient conditions that guarantee the existence of a solu...
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| Format: | Serial |
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2019
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| Series: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciaegyenlet |
| doi: | 10.14232/ejqtde.2019.1.77 |
| Online Access: | http://acta.bibl.u-szeged.hu/64721 |
| Summary: | We study the higher order difference equations of the following form mxn = an f(xσ(n) ) + bn. We are interested in the asymptotic behavior of solutions x of the above equation. Assuming f is a power type function and ∆ myn = bn, we present sufficient conditions that guarantee the existence of a solution x such that xn = yn + o(n s where s ≤ 0 is fixed. We establish also conditions under which for a given solution x there exists a sequence y such that ∆ myn = bn and x has the above asymptotic behavior. |
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| Physical Description: | 1-17 |
| ISSN: | 1417-3875 |