Non-autonomous boundary value problems on the real line
type: Item
instance of: scholarly article
title: Non-autonomous boundary value problems on the real line
zbMATH Open document ID: 1132.34026
author: Barbara Bianconi
author: Francesca Papalini
published in: Discrete and Continuous Dynamical Systems
publication date: 2007-04-05T00:00:00Z
review text: The general non-autonomous boundary value problem \[ (\Phi(x'(t)))' = f(t,x(t),x'(t)), \qquad x(-\infty)=0 , \quad x(+\infty)=1 \] is investigated, where \(\Phi\) is a monotone functional, including the classical \(p\)-Laplacian operator as a particular case. The authors obtain both existence and non-existence results under mild assumptions, which become very efficient criteria when the right-hand side has the product structure \(f(t,x,x')= a(t,x)b(x,x')\), based on the behavior of \(a(t,x)\) as \(| t| \to +\infty\) and \(b(x,y)/\Phi(y)\) as \(y\to 0\). Many examples are presented, both for general functionals \(\Phi\) and for the \(p\)-Laplacian operator.
reviewed by: Cristina Marcelli
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5140548
zbMATH Keywords: nonlinear boundary value problems
zbMATH Keywords: infinite interval
zbMATH Keywords: heteroclinic solutions
zbMATH Keywords: \(p\)-Laplacian operator
MaRDI profile type: Publication
full work available at URL: dcds.2006.15.759
OpenAlex ID: W1969556420
DOI: 10.3934/DCDS.2006.15.759
description: scientific article; zbMATH DE number 5140548