Existence and multiplicity of positive solutions for a fourth-order \(p\)-Laplace equation
type: Item
instance of: scholarly article
title: Existence and multiplicity of positive solutions for a fourth-order \(p\)-Laplace equation
zbMATH Open document ID: 1010.34007
DOI: 10.1023/A:1022851213931
author: Zhanbing Bai
published in: Applied Mathematics and Mechanics. (English Edition)
publication date: 2002-10-23T00:00:00Z
review text: The author studies some existence and multiplicity results on positive solutions to the following one-dimensional fourth-order \(p\)-Laplace equation \(g(u'')''+\lambda a(t) f(u)=0\), \(0<t<1\), with the BV conditions: \(u(0)=u(1)=u''(0)=u''(1)=0\) or \(u(0)=u'(1)=u''(0)=u'''(1)=0\), where \(g(v)=|v|^{p-2}v\), \(p>1\) , \(f(u)\) is nonnegative continuous in \([0,\infty)\) and \(a(t)\) is nonnegative continuous in \((0,1)\) . The techniques used are based on cone compression/extension theorem.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1743796
zbMATH Keywords: nonlinear boundary value problem
zbMATH Keywords: \(p\)-Laplacian
zbMATH Keywords: positive solution
zbMATH Keywords: cone
reviewed by: N. Del Toro
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1743796