On periodic-type solutions of systems of linear ordinary differential equations
type: Item
instance of: scholarly article
title: On periodic-type solutions of systems of linear ordinary differential equations
zbMATH Open document ID: 1077.34020
DOI: 10.1155/S1085337504306159
author: Ivan Kiguradze
published in: Abstract and Applied Analysis
publication date: 2005-04-29T00:00:00Z
full work available at URL: https://eudml.org/doc/51872
review text: The author considers existence and uniqueness of an \(\omega\)-periodic solution of the linear differential system \[ \frac {dx_i}{dt}={\mathcal P}_{i_1}(t)x_1+{\mathcal P}_{i_2}(t)x_2+q_i(t), \quad i=1,2, \] satisfying the conditions \[ x_i(t+\omega)=\Lambda_ix_i(t)\text{ for }t\in\mathbb{R},\quad i=1,2, \] where \(\omega>0\); \(\Lambda_i\in \mathbb{R}^{n_i\times n_i},\) \(i=1,2\), are nonsingular matrices; \(n_1,n_2\) natural numbers; \[ {\mathcal P}_{i_k}:\mathbb{R}\to \mathbb{R}^{n_i\times n_k},\quad i,k=1,2, \] and \(q_i:\mathbb{R}\to \mathbb{R}^{n_i}\), \(i=1,2\), matrix and vector functions, whose components are Lebesgue integrable on each compact interval.
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 2163661
zbMATH Keywords: \(\omega\)-periodic solution
zbMATH Keywords: spectral radius of the matrix
zbMATH Keywords: nonsingular matrix
MaRDI profile type: Publication
OpenAlex ID: W2001525195
Recommended article: Q5487034
Recommended article: Periodic solutions of some linear systems of differential equations
Recommended article: Q3561619
Recommended article: Periodic solutions of a class of nonlinear systems of ordinary differential equations
Recommended article: Q4231495
Recommended article: Q3351725
Recommended article: Q3485216
Recommended article: Q3729364
Recommended article: On Periodic Solutions of One Class of Systems of Differential Equations
Recommended article: Q3705879
description: scientific article; zbMATH DE number 2163661