Perturbations of nonlinear systems of ordinary differential equations
type: Item
instance of: scholarly article
title: Perturbations of nonlinear systems of ordinary differential equations
zbMATH Open document ID: 0588.34040
DOI: 10.1016/0022-247X(84)90151-3
author: Enhao Yang
published in: Journal of Mathematical Analysis and Applications
publication date: 1984-01-01T00:00:00Z
review text: Along with the n dimensional system (1) \(y'=f(t,y)\) the perturbed system (2) \(x'=f(t,x)+g(t,x)\) is considered. Certain refined assumptions are made about estimates of the fundamental matrix solution of the variational system with respect to a solution of system (1), and about g. (The function g need not be ''small'', it may be sublinear or linear.) Under these assumptions theorems are proved concerning the boundedness, the convergence to zero, the ''slowly growingness'', the asymptotic stability, and the uniform asymptotic stability of solutions of (2). These theorems have important implications if applied to the case when (1) is linear.
Mathematics Subject Classification ID: 34D10
Mathematics Subject Classification ID: 34A34
zbMATH DE Number: 3944336
zbMATH Keywords: fundamental matrix solution
zbMATH Keywords: boundedness
zbMATH Keywords: asymptotic stability
zbMATH Keywords: uniform asymptotic stability
reviewed by: M. Farkas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3944336