Existence problems for homoclinic solutions
type: Item
instance of: scholarly article
title: Existence problems for homoclinic solutions
zbMATH Open document ID: 1009.34025
DOI: 10.1155/S108533750200074X
author: Cezar Avramescu
published in: Abstract and Applied Analysis
publication date: 2002-08-13T00:00:00Z
full work available at URL: https://eudml.org/doc/49901
review text: Let \(f: \mathbb{R}\times \mathbb{R}^n\to \mathbb{R}^n\) be a continuous function. The author considers the problem \[ \dot x= f(t,x),\quad x(-\infty)= x(+\infty),\tag{P} \] with \(x(\pm\infty):= \lim_{t\to\pm\infty} x(t)\in \mathbb{R}^n\). The author reduces (P) to a fixed-point problem for a convenient operator defined in the functional space \[ C_l:= \{x: \mathbb{R}\to \mathbb{R}^n\mid \exists x(\pm\infty)\in \mathbb{R}^n\}, \] and then applies the continuation method to establish the existence results for problem (P).
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34C37
Mathematics Subject Classification ID: 47H11
zbMATH DE Number: 1780519
zbMATH Keywords: homoclinic solution
zbMATH Keywords: existence
zbMATH Keywords: isometric isomorphism
zbMATH Keywords: system
zbMATH Keywords: linearizable equation
zbMATH Keywords: topological degree
reviewed by: Ruyun Ma
MaRDI profile type: Publication
OpenAlex ID: W1996151642
description: scientific article; zbMATH DE number 1780519