Bifurcation of singular points of differential-functional equations
type: Item
instance of: scholarly article
title: Bifurcation of singular points of differential-functional equations
zbMATH Open document ID: 0612.34025
DOI: 10.1007/BF01056824
author: I. I. Klevchuk
author: V. I. Fodchuk
published in: Ukrainian Mathematical Journal
publication date: 1986-01-01T00:00:00Z
review text: Bifurcation of singular points of the system \[ (1)\quad dx/dt=L(\epsilon)x_ t+f(t,x_ t,\epsilon) \] is considered, where \(\epsilon\) is a small parameter, L(\(\epsilon)\): \(C\to R^ n\) is a linear continuous functional, \(f(t+T,\phi,\epsilon)=f(t,\phi,\epsilon),\) \(T>0\); \(f(t,\phi,\epsilon)=O(| \phi |^ 2)\) as \(| \phi | \to 0\) and f(t,\(\phi\),\(\epsilon)\) is a functional continuous with respect to t and \(\epsilon\) and four times differentiabe with respect to \(\phi\). A method for finding a solution to (1) is presented.
Mathematics Subject Classification ID: 34C05
Mathematics Subject Classification ID: 34A99
zbMATH DE Number: 3989814
zbMATH Keywords: Bifurcation of singular points
zbMATH Keywords: small parameter
reviewed by: Izabela Foltyńska
MaRDI profile type: Publication
cites work: Q3992752
cites work: Q5581894
cites work: Integral sets and the reduction principle for differential-functional equations
cites work: Q3948194
cites work: Q5509213
cites work: Q3913687
cites work: Integral averaging and bifurcation
description: scientific article; zbMATH DE number 3989814