Upper and lower solutions for \(\Phi\)-Laplacian third-order BVPs on the half line
type: Item
instance of: scholarly article
zbMATH Open document ID: 1319.34038
DOI: 10.4067/S0719-06462014000100010
author: Smail Djebali
author: Ouiza Saifi
publication date: 2014-08-26T00:00:00Z
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B40
Mathematics Subject Classification ID: 47H10
Mathematics Subject Classification ID: 34B16
zbMATH DE Number: 6334297
zbMATH Keywords: third order equation
zbMATH Keywords: boundary value problem on the half-line
zbMATH Keywords: \(\Phi\)-Laplacian
zbMATH Keywords: singular problem
zbMATH Keywords: positive solution
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: fixed point
MaRDI profile type: Publication
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full work available at URL: s0719-06462014000100010
OpenAlex ID: W2040679704
title: Upper and lower solutions for \(\Phi\)-Laplacian third-order BVPs on the half line
published in: Cubo
review text: The authors study the existence of positive solutions for third-order boundary value problems of the type NEWLINE\[NEWLINE\begin{aligned} (\Phi(-x''(t)))' + f (t, x(t)) = 0, \quad t \in (0,+\infty), \\ x(0)=\mu x'(0), \;x'(+\infty)=x''(+\infty)=0, \end{aligned}NEWLINE\]NEWLINE where \(\mu\geq0\), \(f\) is a continuous map and \(\Phi:\mathbb{R}\to\mathbb{R}\) is a continuous, increasing homeomorphism such that \(\Phi(0)=0\). The map \(\Phi\), the so-called \(\Phi\)-Laplacian, is a generalization of the one-dimensional \(p\)-Laplacian. The map \(f\) verifies some monotonicity assumption and may be singular at \(0\).NEWLINENEWLINEUsing the method of upper and lower solutions and fixed point techniques, the existence of at least one positive solution is proved. The result is illustrated by a concrete example.
reviewed by: Alessandro Calamai
description: scientific article; zbMATH DE number 6334297