Inequalities for solutions of multipoint boundary value problems
type: Item
instance of: scholarly article
title: Inequalities for solutions of multipoint boundary value problems
zbMATH Open document ID: 0954.34010
author: Paul W. Eloe
author: Johnny Henderson
published in: Rocky Mountain Journal of Mathematics
publication date: 2000-09-04T00:00:00Z
full work available at URL: CONT29-3.html
review text: The concept of concavity is generalized to functions \(y\) satisfying \(y^{(n)}\geq 0\), and homogeneous multipoint boundary conditions, \[ y^{(j)}(a_i)=0,\;j=0,\cdots,n_i,i=1,\cdots,k, \] with \(0=a_1<\cdots<a_k=1\), and \(\sum_{i=1}^k n_i=n\). A piecewise polynomial, which bounds the function \(y\) below, is constructed and is employed to obtain \((-1)^{\alpha_i}y(t)\geq ||y||a^m\) for some constants \(a, m, \alpha_i,i=1,\cdots,k-1\). This inequality is useful in applications of certain cone theoretic fixed point theorems.
Mathematics Subject Classification ID: 34B10
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 1439638
zbMATH Keywords: inequalities for solutions
zbMATH Keywords: multipoint boundary value problems
reviewed by: Yujun Dong
MaRDI profile type: Publication
OpenAlex ID: W2073099647
cites work: Q5848416
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DOI: 10.1216/RMJM/1181071611
description: scientific article; zbMATH DE number 1439638