Asymptotic stability of two dimensional systems of linear difference equations and of second order half-linear differential equations with step function coefficients
We give a sufficient condition guaranteeing asymptotic stability with respect to $x$ for the zero solution of the half-linear differential equation \[x''|x'|^{n-1} + q(t)|x|^{n-1}x=0, \qquad 1\le n \in \mathbb{R},\] with step function coefficient $q$. The geometric method of the proof...
Main Authors: | , |
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Format: | Article |
Language: | English |
Published: |
University of Szeged
2011-06-01
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Series: | Electronic Journal of Qualitative Theory of Differential Equations |
Subjects: | |
Online Access: | http://www.math.u-szeged.hu/ejqtde/periodica.html?periodica=1¶mtipus_ertek=publication¶m_ertek=784 |
Summary: | We give a sufficient condition guaranteeing asymptotic stability with respect to $x$ for the zero solution of the half-linear differential equation \[x''|x'|^{n-1} + q(t)|x|^{n-1}x=0, \qquad 1\le n \in \mathbb{R},\] with step function coefficient $q$. The geometric method of the proof can be applied also to two dimensional systems of linear non-autonomous difference equations. The application gives a new simple proof for a sharpened version of \'A. Elbert's asymptotic stability theorems for such difference equations and linear second order differential equations with step function coefficients. |
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ISSN: | 1417-3875 1417-3875 |