To the question of stability with respect to nonlinear approximation
type: Item
instance of: scholarly article
title: To the question of stability with respect to nonlinear approximation
zbMATH Open document ID: 0942.34044
DOI: 10.1007/BF02675931
published in: Siberian Mathematical Journal
publication date: 2000-04-13T00:00:00Z
review text: The system of ordinary differential equations \[ \dot{x}_s = f_s (x) + \sum_{j=1}^{k} b_{sj} (t) h_j (x), \qquad s = 1,\ldots,n, \tag{1} \] is considered. Here, \(f_s(x)\) and \(h_j(x)\) are continuously differentiable homogeneous functions of order \(\mu\) and \(\sigma\) respectively; \(\mu >1\) and \(\sigma >1\) are rational numbers with odd denominators. The functions \(b_{sj} (t)\) are continuous and bounded for all \(t \geq 0\). The author obtains conditions under which the asymptotic stability of the trivial solution to (1) follows from the asymptotic stability of the trivial solution to the nonperturbed system \[ \dot{x}_s = f_s (x), \qquad s = 1,\ldots,n . \]
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1431680
zbMATH Keywords: Lyapunov function
zbMATH Keywords: asymptotic stability
author: A. Yu. Aleksandrov
MaRDI profile type: Publication
cites work: Q5180897
cites work: Q5803517
cites work: The stability of equilibrium of nonstationary systems
cites work: Q5594821
Wikidata QID: Q126211075
full work available at URL: https://doi.org/10.1007/bf02675931
OpenAlex ID: W2129886080
description: scientific article; zbMATH DE number 1431680