Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations
type: Item
instance of: scholarly article
title: Homoclinic solutions for autonomous ordinary differential equations with nonautonomous perturbations
zbMATH Open document ID: 0840.34045
author: Joseph Gruendler
published in: Journal of Differential Equations
publication date: 1995-10-29T00:00:00Z
review text: Consider a system of the form \(x'= f_0(x)+ \mu_1 f_1(x, \mu, t)+ \mu_2 f_2(x, \mu, t)\), where \(x\in \mathbb{R}^n\), \(\mu= (\mu_1, \mu_2)\in \mathbb{R}^2\). It is assumed that for \(\mu= 0\) there exists a homoclinic trajectory. The author applies the Lyapunov-Schmidt method to construct a bifurcation equation \(H= 0\). This equation determines the bifurcation diagram for homoclinic solutions.
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 34C23
Mathematics Subject Classification ID: 34D10
zbMATH DE Number: 810060
zbMATH Keywords: Lyapunov-Schmidt method
zbMATH Keywords: bifurcation equation
zbMATH Keywords: homoclinic solutions
reviewed by: Sergei Yu. Pilyugin
MaRDI profile type: Publication
full work available at URL: jdeq.1995.1136
OpenAlex ID: W1970006304
DOI: 10.1006/JDEQ.1995.1136
description: scientific article; zbMATH DE number 810060