Small solutions of the damped half-linear oscillator with step function coefficients
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...
Elmentve itt :
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| Dokumentumtípus: | Folyóirat |
| Megjelent: |
2018
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| Sorozat: | Electronic journal of qualitative theory of differential equations : special edition
3 No. 46 |
| Kulcsszavak: | Differenciálegyenlet, Oszcilláció - differenciálegyenlet |
| Online Access: | http://acta.bibl.u-szeged.hu/55716 |
| Tartalmi kivonat: | 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 |