Positive solutions of \(2m\)th-order boundary value problems
type: Item
instance of: scholarly article
title: Positive solutions of \(2m\)th-order boundary value problems
zbMATH Open document ID: 1019.34019
DOI: 10.1016/S0893-9659(02)00040-X
author: Chuan J. Chyan
author: Johnny Henderson
published in: Applied Mathematics Letters
publication date: 2002-09-03T00:00:00Z
review text: By application of the Guo-Krasnosel'skii fixed-point theorem in a cone, the authors prove the existence of a positive solution to two boundary values problems for the equation \[ (-1)^m y^{(2m)}(t)=f(t, y(t), y''(t), \ldots, y^{2(m-1)}(t)), \] where \(f\) is either superlinear or sublinear. The boundary conditions are \[ \begin{aligned} y^{2 i}(0)&= 0=y^{2 i}(1), \quad 0 \leq i \leq m-1, \qquad\text{ or }\\ y^{2 i}(0)&= 0=y^{2 i +1 }(1), \quad 0 \leq i \leq m-1.\end{aligned} \] {}.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 1794944
zbMATH Keywords: positive solution
zbMATH Keywords: existence
zbMATH Keywords: ordinary differential equation
zbMATH Keywords: \(2m\)th order
zbMATH Keywords: boundary value problem
reviewed by: Leonid Lebedev
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1794944