Asymptotic properties of solutions of nonlinear vector initial value problem on the infinite interval
type: Item
instance of: scholarly article
title: Asymptotic properties of solutions of nonlinear vector initial value problem on the infinite interval
zbMATH Open document ID: 0626.34005
DOI: 10.1007/BF02017979
author: Shengiang Kang
author: Anjiang Zhang
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 1987-01-01T00:00:00Z
review text: We study initial value problems on the infinite interval: \[ (1)\quad dx/dt=f(t,x,y;\epsilon),\quad x(0,\epsilon)=\xi (\epsilon),\quad \epsilon (dy/dt)=g(t,x,y;\epsilon),\quad y(0,\epsilon)=\eta (\epsilon) \] where \(x,f\in E^ m\), \(y,g\in E^ n\), \(\epsilon\) are real small positive parameters, \(0\leq t<+\infty\). If \(g_ y(t)\) is nonsingular and under other assumptions, we prove that there are serial \((k+m^*)\)-dimensional manifolds \(\{S_ R(\epsilon)\}\in E^{m+n}\) such that (1) degenerates regularly provided \((\xi (\epsilon),\eta (\epsilon))\in S_ R(\epsilon)\). Besides, the R-order asymptotic expansions of solutions are constructed, and their errors are estimated.
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 4017353
zbMATH Keywords: first order differential equation
zbMATH Keywords: small positive parameters
zbMATH Keywords: asymptotic expansions
MaRDI profile type: Publication
cites work: Q5814121
cites work: Q5825916
cites work: Singular Perturbations on the Infinite Interval
cites work: Stability in systems with parameter
cites work: Singular perturbations of nonlinear systems of differential equations related to conditional stability
cites work: Q5850715
cites work: Properties of solutions of ordinary differential equations with small parameters
cites work: Dichotomies and reducibility
cites work: Singular perturbations of initial value problems over a finite interval
full work available at URL: https://doi.org/10.1007/bf02017979
OpenAlex ID: W2059018209
description: scientific article; zbMATH DE number 4017353