Optimal existence theory for single and multiple positive solutions to second order Neumann boundary value problems
type: Item
instance of: scholarly article
title: Optimal existence theory for single and multiple positive solutions to second order Neumann boundary value problems
zbMATH Open document ID: 1070.34038
author: Xiaoyue Li
author: Daqing Jiang
published in: Indian Journal of Pure \& Applied Mathematics
publication date: 2005-03-07T00:00:00Z
review text: The paper deals with Neumann boundary value problems of the form \[ -u''+\rho_1^2 u =f(t,u),\quad u'(0)=u'(1)=0, \tag{1} \] or \[ u''+\rho_2^2 u =f(t,u),\quad u'(0)=u'(1)=0, \tag{2} \] where \(f:[0,1]\times [0,\infty)\) is nonnegative continuous, and \(\rho_1>0\), \(\rho_2\in (0,\pi/2)\). The authors provide sufficient conditions for the existence of at least one positive solution of (1) or (2) and for the existence of at least two positive solutions of (1) or (2). These conditions are formulated in terms of an asymptotic behaviour of \({f(t,x)\over x}\) near \(0\) and \(\infty\). The proofs are based on Krasnoselskii's fixed-point theorem in cones.
reviewed by: Irena Rachůnková
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 2141228
zbMATH Keywords: Neumann boundary value problem
zbMATH Keywords: positive solutions
zbMATH Keywords: existence
zbMATH Keywords: multiplicity
zbMATH Keywords: fixed-point theorem in cones
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 2141228