On transitional solutions of second order nonlinear differential equations
type: Item
instance of: scholarly article
title: On transitional solutions of second order nonlinear differential equations
zbMATH Open document ID: 1140.34347
author: Luisa Malaguti
author: Cristina Marcelli
author: Nino Partsvania
published in: Journal of Mathematical Analysis and Applications
publication date: 2005-03-08T00:00:00Z
review text: Consider the scalar differential equation \[ u''= f(t,u,u'),\tag{\(*\)} \] where \(f\) is continuous and satisfies \[ f(t,0,0)\equiv 0,\quad f(t,1,0)\equiv 0\quad\text{for }t\in \mathbb{R}. \] The authors ask for a solution of \((*)\) satisfying \[ \lim_{t\to-\infty} u(t)= 0,\quad \lim_{t\to\infty} u(t)= 1,\quad 0\leq u(t)\leq 1\quad\text{for }t\in\mathbb{R}.\tag{\(**\)} \] They derive conditions guaranteeing that the boundary value problem \((*)\) and \((**)\) has at least one solution which is monotone increasing. The proofs are based on comparison principles. The existence of such heteroclinic solutions is related to the existence of traveling wave solutions to partial differential equations.
reviewed by: Klaus R. Schneider
Mathematics Subject Classification ID: 34B40
zbMATH DE Number: 2141754
MaRDI profile type: Publication
full work available at URL: j.jmaa.2004.08.032
OpenAlex ID: W2063853301
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DOI: 10.1016/J.JMAA.2004.08.032
description: scientific article; zbMATH DE number 2141754