Existence and stability of almost-periodic solutions of quasi-linear differential equations with deviating argument.
type: Item
instance of: scholarly article
title: Existence and stability of almost-periodic solutions of quasi-linear differential equations with deviating argument.
zbMATH Open document ID: 1082.34538
published in: Applied Mathematics Letters
publication date: 2005-03-07T00:00:00Z
review text: For the equation \[ x'(t)= A(t)x(t)+ f(t,x(t),\dots,x(t-\tau_k(t))), \] the existence of an almost-periodic solution is shown under the following assumptions: \(A(t)\) is an \(n\times n\)-matrix, almost-periodic in \(t\); \(\tau_j\) almost-periodic; \(f(t,u_0,\dots,u_k)\) is almost-periodic in \(t\) locally uniformly in the \(u_j\) and Lipschitzian in the \(u_j\), with sufficiently small Lipschitz constant; \(x'= A(t)x\) satisfies an exponential dichotomy. Under some additional assumptions and with \(\tau_j\geq 0\), such a solution is shown to be exponentially stable.
reviewed by: Hans Günzler
Mathematics Subject Classification ID: 34K14
Mathematics Subject Classification ID: 34K20
zbMATH DE Number: 2140801
zbMATH Keywords: Quasi-Linear system
zbMATH Keywords: Almost-periodic solutions
zbMATH Keywords: Deviating argument
zbMATH Keywords: Stability
author: M. Akhmet
MaRDI profile type: Publication
full work available at URL: j.aml.2003.08.012
OpenAlex ID: W2087384923
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DOI: 10.1016/J.AML.2003.08.012
description: scientific article; zbMATH DE number 2140801