Positive solution for three-point boundary value problems with sign changing nonlinearities.
type: Item
instance of: scholarly article
title: Positive solution for three-point boundary value problems with sign changing nonlinearities.
zbMATH Open document ID: 1071.34024
DOI: 10.1016/S0893-9659(04)90088-2
author: Jingli Ren
author: Weigao Ge
published in: Applied Mathematics Letters
publication date: 2005-02-25T00:00:00Z
review text: The authors obtain an existence result on one positive solution of the second-order three-point boundary value problem \[ u''(t)=h(t)f(t,\,u(t)),\qquad 0\leq t\leq 1,\quad u(0)-\beta u'(0)=0,\qquad u(1)=\alpha u(\eta), \] where \(f:[0,\,1]\times[0,\,\infty)\to \mathbb{R}\) is continuous, \(h:[0,\,1]\to [0,\,\infty)\) is Lebesgue integrable and \(\int_0^1h(t)\,dt>0\), \(\eta\in (0,\,1)\), \(0<\alpha<1\) and \(\beta>0\). The main trait of this paper is that it allows \(f\) to change sign. The argument is based on the topological degree theory in cones.
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 2138606
zbMATH Keywords: three-point boundary value problem
zbMATH Keywords: Green's function
zbMATH Keywords: topology degree in cones
MaRDI profile type: Publication
cites work: Q3820939
cites work: Q3712561
cites work: On an M-point boundary value problem
cites work: A sharper condition for the solvability of a three-point second order boundary value problem
cites work: A generalized multi-point boundary value problem for second order ordinary differential equations
cites work: Criteria for multiple solutions to difference and partial difference equations subject multipoint conjugate conditions
cites work: Q4264050
cites work: Positive solutions of three-point nonlinear second order boundary value problem
full work available at URL: s0893-9659(04)90088-2
OpenAlex ID: W2073015444
description: scientific article; zbMATH DE number 2138606