Existence of positive solutions for \(m\)-Laplacian boundary value problems
type: Item
instance of: scholarly article
title: Existence of positive solutions for \(m\)-Laplacian boundary value problems
zbMATH Open document ID: 0952.34015
DOI: 10.1016/S0893-9659(98)00164-5
author: Fu-Hsiang Wong
published in: Applied Mathematics Letters
publication date: 2000-12-28T00:00:00Z
review text: The author gives some sufficient conditions for the existence of positive solutions to the boundary value problem \[ (|u'(t) |^{m-2}u'(t))' + f(t,u(t)) = 0, \quad 0 < t < 1, \quad u'(0) = u(1) = 0, \] with \(m \geq 2\), \(f: [0,1) \times (0,\infty) \rightarrow (0,\infty)\) is locally Lipschitz continuous and \(f(t,u)/u^{m-1}\) is strictly decreasing in \(u\), for each fixed \(t\). The proofs are based on the shooting method.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 35J65
zbMATH DE Number: 1369365
zbMATH Keywords: \(m\)-Laplacian
zbMATH Keywords: boundary value problems
zbMATH Keywords: positive solutions
zbMATH Keywords: existence
zbMATH Keywords: locally Lipschitz continuous
zbMATH Keywords: shooting method
reviewed by: Antonio Cañada
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1369365