On the stability of periodic solutions to nonlinear differential systems
type: Item
instance of: scholarly article
zbMATH Open document ID: 0987.34034
publication date: 2001-12-18T00:00:00Z
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 1683432
zbMATH Keywords: differential system
zbMATH Keywords: periodic solution
zbMATH Keywords: stability
author: V. N. Laptinsky
MaRDI profile type: Publication
title: On the stability of periodic solutions to nonlinear differential systems
published in: Trudy Instituta Matematiki
review text: The author considers the system of differential equations NEWLINE\[NEWLINE \frac{dx}{dt} = f(t,x),\tag{1} NEWLINE\]NEWLINE with \(x\in \mathbb{R}^n\), \(f(t,x)\in C_{tx}^{(0,1)} (\mathbb{R}\times \mathbb{R}^n)\), \(f(t+\omega,x) = f(t,x)\), and the corresponding first approximation system NEWLINE\[NEWLINE \frac{du}{dt} = A(t)u,\tag{2} NEWLINE\]NEWLINE with \(A(t) = f_x'(t,\eta(t))\) and \(\eta(t)\) is an \(\omega\)-periodic solution to system (1). General coefficient criteria for the asymptotic stability of system (1) are established in terms of the matrix of fundamental solutions to system (2). Some corollaries are presented.
reviewed by: A. A. Martynyuk
description: scientific article; zbMATH DE number 1683432