Two positive solutions for second-order quasilinear differential equation boundary value problems with sign changing nonlinearities
type: Item
instance of: scholarly article
title: Two positive solutions for second-order quasilinear differential equation boundary value problems with sign changing nonlinearities
zbMATH Open document ID: 1062.34019
author: Yanping Guo
author: Ji-Wei Tian
published in: Journal of Computational and Applied Mathematics
publication date: 2004-08-16T00:00:00Z
review text: The authors study the sovability of boundary value problems for the equation \[ \bigl(\Phi(y')\bigr)'+q(t)f(t,y)=0,\;\;0<t<1, \] with boundary conditions \[ y(0)=y(1)=0\quad\text{or}\quad y(0)=y'(1)=0, \] where \(\Phi(v)=| v|^{p-2}v, p>1,\quad q:(0,1)\to[0,\infty)\) is continuous, \(q(t)\not\equiv0\) on any subinterval of \((0,1),\) \(\int_0^1q(t)dt<\infty\), and \(f\) is allowed to change sign, i.e., \(f:[0,1]\times[0,\infty)\to[-M,\infty)\) (with any constant \(M>0\)) is continuous and such that \(f(t,0)\geq0\) \((\not\equiv0)\) for \(t\in[0,1].\) The authors have imposed growth conditions on \(f\) to obtain at least two positive solutions for the considered boundary value problems. Moreover, they have applied a new fixed-point theorem in cones.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2091414
zbMATH Keywords: boundary value problems
zbMATH Keywords: p-Laplacian
zbMATH Keywords: existence
zbMATH Keywords: positive symmetric solutions
zbMATH Keywords: fixed-point theorem in cones
reviewed by: Petio S. Kelevedjiev
MaRDI profile type: Publication
full work available at URL: j.cam.2003.12.029
OpenAlex ID: W2050652885
Wikidata QID: Q115359898
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DOI: 10.1016/J.CAM.2003.12.029
description: scientific article; zbMATH DE number 2091414