Positivity conditions and bounds for Green's functions for higher order two-point BVP
type: Item
instance of: scholarly article
title: Positivity conditions and bounds for Green's functions for higher order two-point BVP
zbMATH Open document ID: 1315.34038
published in: Central European Journal of Mathematics
publication date: 2012-01-16T00:00:00Z
review text: The author studies the higher order two-point boundary value problem \[ \sum_{k=0}^n a_{n-k}(x) D^k u(x) = f(x), \quad 0<x<1, \] \[ u^{(2k)}(0) = u^{(2k)}(1) = 0, \quad k=0,1,\cdots,n-1. \] Here \(a_k(x)\), \(k=1,2,\cdots,n\), are real continuous functions, \(a_0(x)\equiv 1\), and \(D=-d^2/dx^2\). The author proves some sufficient conditions for the positivity of Green's function of the problem. He also obtains a set of upper and lower bounds for Green's function. At the end of the paper, an existence result for at least one positive solution for the problem is proved.
reviewed by: Bo Yang
Mathematics Subject Classification ID: 34B27
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 5997988
zbMATH Keywords: Green's function
zbMATH Keywords: Positivity
zbMATH Keywords: Lidstone boundary value problem
author: Michael I. Gil'
MaRDI profile type: Publication
full work available at URL: s11533-011-0052-9
OpenAlex ID: W2084225079
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DOI: 10.2478/S11533-011-0052-9
description: scientific article; zbMATH DE number 5997988