Monotone iterative technique and positive solutions of lidstone boundary value problems.
type: Item
instance of: scholarly article
title: Monotone iterative technique and positive solutions of lidstone boundary value problems.
zbMATH Open document ID: 1049.34028
DOI: 10.1016/S0096-3003(01)00316-2
published in: Applied Mathematics and Computation
publication date: 2003-09-09T00:00:00Z
review text: Consider the boundary value problem \[ (-1)^n w^{(2n)} (t) = f(t,w(t)), \quad 0 \leq t \leq 1,\quad w^{(2i)} (0) = w^{(2i)} (1) = 0, \quad 0 \leq i \leq n-1, \tag{\(*\)} \] under the conditions (i) \(f:[0,1] \times [0,+\infty) \rightarrow [0,+\infty)\) is continuous. (ii) \(f(t,.)\) is nondecreasing for any \(t \in [0,1].\) (iii) \(f(t,w)=f(1-t,w)\) for all \(t\in [0,1], w\in [0,\infty).\) A solution of \((*)\) is said to be symmetric, if \(w(t)=w(1-t)\). By using the monotone iterative technique, the author proves the existence of \(N\) symmetric positive solutions of \((*)\).
Mathematics Subject Classification ID: 34B18
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34A45
zbMATH DE Number: 1977982
zbMATH Keywords: lidstone boundary value problem
zbMATH Keywords: symmetric positive solution
zbMATH Keywords: existence and multiplicity
zbMATH Keywords: monotone iterative technique
author: Qingliu Yao
reviewed by: Klaus R. Schneider
MaRDI profile type: Publication
cites work: Q3732891
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full work available at URL: s0096-3003(01)00316-2
OpenAlex ID: W4248029119
description: scientific article; zbMATH DE number 1977982