The continuous dependence of periodic solutions for the periodic quasilinear ordinary differential system containing a parameter
type: Item
instance of: scholarly article
title: The continuous dependence of periodic solutions for the periodic quasilinear ordinary differential system containing a parameter
zbMATH Open document ID: 0734.34032
DOI: 10.1016/0022-247X(91)90224-N
author: Seiji Saito
author: Minoru Yamamoto
published in: Journal of Mathematical Analysis and Applications
publication date: 1991-01-01T00:00:00Z
review text: Let A(t,x,\(\lambda\)) be a real \(n\times n\) matrix continuous on \({\mathbb{R}}\times {\mathbb{R}}^ n\times [-\lambda_ 0,\lambda_ 0]\) with T- periodicity in t, F(t,x,\(\lambda\)) an \({\mathbb{R}}^ n\)-valued function continuous on \({\mathbb{R}}\times {\mathbb{R}}^ n\times [-\lambda_ 0,\lambda_ 0]\) with T-periodicity in t, where \(\lambda_ 0>0\) and f(t) an \({\mathbb{R}}^ n\)-valued function continuous on \({\mathbb{R}}\) and T-periodic in t. The authors present results for the dependence on \(\lambda\) of T- periodic solutions for the T-periodic quasilinear ordinary differential system \(x'=A(t,x,\lambda)x+\lambda F(t,x,\lambda)+f(t)\) assuming that there exists a unique T-periodic solution of the associated linear system \(x'=B(t)x+f(t),\) where B(t) is a real \(n\times n\) matrix continuous on \({\mathbb{R}}\) and T-periodic.
Mathematics Subject Classification ID: 34C25
zbMATH DE Number: 4214413
zbMATH Keywords: dependence on parameter
zbMATH Keywords: periodic solutions
zbMATH Keywords: quasilinear ordinary differential system
zbMATH Keywords: associated linear system
reviewed by: Olusola Akinyele
MaRDI profile type: Publication
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cites work: Quasilinear equations and equations with large nonlinearities
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full work available at URL: 0022-247x(91)90224-n
OpenAlex ID: W1984159568
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description: scientific article; zbMATH DE number 4214413