Dénes Attila and Székely László: Small solutions of the damped half-linear oscillator with step function coefficients. (2018)
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Abstract
In this paper we consider the damped half-linear oscillator x 00|x 0 n−1 + c(t)|x 0 n−1 x 0 + a(t)|x| n−1 x = 0, n ∈ R We give a sufficient condition guaranteeing the existence of a small solution, that is a non-trivial solution which tends to 0 as t tends to infinity, in the case when both damping and elasticity coefficients are step functions. With our main theorem we not just generalize the corresponding theorem for the linear case n = 1, but we even sharpen Hatvani’s theorem concerning the undamped half-linear differential equation. Keywords: small solution, asymptotic stability, half-linear differential equation, step function coefficients, damping, difference equations.
| Item Type: | Journal |
|---|---|
| Publication full: | Electronic journal of qualitative theory of differential equations |
| Date: | 2018 |
| Number: | 46 |
| ISSN: | 1417-3875 |
| Page Range: | pp. 1-13 |
| DOI: | 10.14232/ejqtde.2018.1.46 |
| Uncontrolled Keywords: | Differenciálegyenlet, Oszcilláció - differenciálegyenlet |
| Additional Information: | Bibliogr.: p. 11-13. ; összefoglalás angol nyelven |
| Date Deposited: | 2019. Jun. 03. 06:07 |
| Last Modified: | 2021. Sep. 16. 10:42 |
| URI: | http://acta.bibl.u-szeged.hu/id/eprint/58139 |
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