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...

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Bibliographic Details
Main Authors: Dénes Attila
Székely László
Format: Serial
Published: 2018
Series: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
Description
Summary: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.
Physical Description:1-13
ISSN:1417-3875