Quasiperiodic solutions of linear nonhomogeneous differential equations
type: Item
instance of: scholarly article
title: Quasiperiodic solutions of linear nonhomogeneous differential equations
zbMATH Open document ID: 1008.34035
DOI: 10.1023/A:1019230301399
author: A. K. Demenchuk
published in: Differential Equations
publication date: 2001-01-01T00:00:00Z
review text: Consider the linear nonhomogeneous differential equation \(\dot x= A(t)x+ \varphi(t)\), \(x\in\mathbb{R}^n\), where \(A(t)\) is a quasiperiodic \(n\times n\)-matrix with frequency basis \(\nu\) and \(\varphi(t)\) is a quasiperiodic \(n\)-vector with frequency basis \(\mu\). Assume that the system has a nonhomogeneity in the form of a trigonometric polynomial whose frequency basis \(\mu\), together with the frequency matrix \(\nu\), forms a rationally linearly independent set. The author derives conditions for the existence of quasiperiodic solutions with frequency basis \(\mu\) and indicates the form of such solutions.
Mathematics Subject Classification ID: 34C27
Mathematics Subject Classification ID: 34A30
Mathematics Subject Classification ID: 34C29
zbMATH DE Number: 1758748
zbMATH Keywords: quasiperiodic solutions
zbMATH Keywords: linear differential equations
MaRDI profile type: Publication
full work available at URL: a:1019230301399
OpenAlex ID: W22722146
description: scientific article; zbMATH DE number 1758748