Positive solutions for equations and systems with \(p\)-Laplace-like operators
type: Item
instance of: scholarly article
title: Positive solutions for equations and systems with \(p\)-Laplace-like operators
zbMATH Open document ID: 1185.34028
published in: Advances in Differential Equations
publication date: 2009-06-30T00:00:00Z
review text: The authors consider the existence of positive solutions of \[ \big( \phi(u') \big)' + f(t, u) = 0, \quad t \in (0, 1), \] \[ \theta(u(0)) = \beta \theta (u'(0)), \] \[ \theta(u(1)) = -\delta \theta (u'(1)), \] where \(\beta, \delta \geq 0\), as well as related boundary value problems. Here, \(\phi\) and \(\theta\) are odd increasing homeomorphisms and \(f:[0, 1] \times [0, \infty) \to [0, \infty)\) is continuous. They prove three theorems on existence using a maximum principle and the Leray-Schauder degree. In each theorem, they assume that the nonlinear term \(f\) is either super-linear or sub-linear. Additionally, they need to assume that limits involving ratios of the form \(\frac{\theta(\tau s)}{\theta(s)}\) are positive and tend to either \(0\) or \(\infty\).
reviewed by: Eric R. Kaufmann
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 47N20
zbMATH DE Number: 5572584
zbMATH Keywords: Leray-Schauder degree
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: positive solution
author: Marta Garcia-Huidobro
author: Raúl Manásevich
author: James Robert jun. Ward
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5572584