Small solutions of the damped half-linear oscillator with step function coefficients
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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2018
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| Sorozat: | Electronic journal of qualitative theory of differential equations
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| Kulcsszavak: | Differenciálegyenlet, Oszcilláció - differenciálegyenlet |
| doi: | 10.14232/ejqtde.2018.1.46 |
| Online Access: | http://acta.bibl.u-szeged.hu/58139 |
| Tartalmi kivonat: | 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. |
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| Terjedelem/Fizikai jellemzők: | 1-13 |
| ISSN: | 1417-3875 |