Bifurcation equation for planar systems of differential equations
type: Item
instance of: scholarly article
title: Bifurcation equation for planar systems of differential equations
zbMATH Open document ID: 0671.34039
DOI: 10.1007/BF00948960
author: Franz Spirig
published in: ZAMP. Zeitschrift für angewandte Mathematik und Physik
publication date: 1988-01-01T00:00:00Z
review text: The author establishes conditions for the existence of small periodic solutions of the equations \[ \dot x=\alpha (\epsilon)x- y+g(x,y,\epsilon),\quad \dot y=x+\alpha (\epsilon)y+h(x,y,\epsilon) \] and \(\ddot y-2\alpha(\epsilon)\dot y+y= f(\dot y,y,\epsilon),\) where \(g=O(x^ 2+y^ 2)\), \(h=O(x^ 2+y^ 2)\) and \(f=O(\dot y^ 2+y^ 2)\). He also discusses their stability.
Mathematics Subject Classification ID: 34C25
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 4097840
zbMATH Keywords: small periodic solutions
Wikidata QID: Q115394816
MaRDI profile type: Publication
cites work: Q3948194
cites work: Existence of small periodic solutions of ordinary differential equations in \(\mathbb{R}^2\)
cites work: Q3886065
cites work: Q4769286
cites work: Q5345151
cites work: Q5182723
description: scientific article; zbMATH DE number 4097840