On the number of positive solutions for a four-point boundary value problem with generalized Laplacian
type: Item
instance of: scholarly article
title: On the number of positive solutions for a four-point boundary value problem with generalized Laplacian
zbMATH Open document ID: 1476.34076
author: Tingzhi Cheng
author: Xianghui Xu
published in: Journal of Fixed Point Theory and Applications
publication date: 2021-08-12T00:00:00Z
review text: In this paper, the authors study the four-point boundary value problem of a nonlinear ordinary differential equation with generalized Laplacian \[ \begin{cases} -\phi(u')'=\lambda h(t)f(t,u), ~ t\in (0,1),\\ u(0) = \alpha u(\xi), u(1) = \beta u(\eta), \end{cases} \] where \(\phi: \mathbb{R}\to \mathbb{R}\) is an odd increasing homeomorphism, \(\lambda > 0,\) \( 0 \le \alpha, \beta < 1,\) \( 0 <\xi < \eta < 1,\) \(f: [0,1]\times [0,\infty)\to [0,\infty)\) is continuous, \(h\not\equiv 0\) on any subinterval in \((0, 1)\) and \(h\) may have a singularity at \(t = 0\) and/or \(t = 1.\) The relations between the number of positive solutions and two different kinds of asymptotic behaviors of the nonlinearity at \(0\) and \(\infty\) were obtained, by using the fixed point theorem of expansion/compression of a cone and Schauder's fixed point theorem.
reviewed by: Sotiris K. Ntouyas
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B16
Mathematics Subject Classification ID: 47N20
Mathematics Subject Classification ID: 34B10
zbMATH DE Number: 7381166
zbMATH Keywords: Four-point boundary value problem
zbMATH Keywords: generalized Laplacian
zbMATH Keywords: singular weight
zbMATH Keywords: positive solution
zbMATH Keywords: fixed point
MaRDI profile type: Publication
full work available at URL: s11784-021-00883-z
OpenAlex ID: W3183747452
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DOI: 10.1007/S11784-021-00883-Z
description: scientific article; zbMATH DE number 7381166