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 :
| Szerzők: | |
|---|---|
| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2018
|
| Sorozat: | Electronic journal of qualitative theory of differential equations
|
| Kulcsszavak: | Differenciálegyenlet, Oszcilláció - differenciálegyenlet |
| doi: | 10.14232/ejqtde.2018.1.46 |
| Online Access: | http://acta.bibl.u-szeged.hu/58139 |
| LEADER | 01507nas a2200217 i 4500 | ||
|---|---|---|---|
| 001 | acta58139 | ||
| 005 | 20210916104248.0 | ||
| 008 | 190603s2018 hu o 0|| zxx d | ||
| 022 | |a 1417-3875 | ||
| 024 | 7 | |a 10.14232/ejqtde.2018.1.46 |2 doi | |
| 040 | |a SZTE Egyetemi Kiadványok Repozitórium |b hun | ||
| 041 | |a zxx | ||
| 100 | 1 | |a Dénes Attila | |
| 245 | 1 | 0 | |a Small solutions of the damped half-linear oscillator with step function coefficients |h [elektronikus dokumentum] / |c Dénes Attila |
| 260 | |c 2018 | ||
| 300 | |a 1-13 | ||
| 490 | 0 | |a Electronic journal of qualitative theory of differential equations | |
| 520 | 3 | |a 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. | |
| 695 | |a Differenciálegyenlet, Oszcilláció - differenciálegyenlet | ||
| 700 | 0 | 1 | |a Székely László |e aut |
| 856 | 4 | 0 | |u http://acta.bibl.u-szeged.hu/58139/1/ejqtde_2018_046.pdf |z Dokumentum-elérés |