Solutions of 2\(n\)th Lidstone boundary value problems and dependence on higher order derivatives
type: Item
instance of: scholarly article
title: Solutions of 2\(n\)th Lidstone boundary value problems and dependence on higher order derivatives
zbMATH Open document ID: 1029.34019
DOI: 10.1016/S0022-247X(03)00011-8
author: Zhanbing Bai
author: Weigao Ge
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-05-25T00:00:00Z
review text: The authors consider the Lidstone boundary value problem \[ \begin{gathered} (-1)^nu^{2n}(x)= f(x, u(x), u''(x),\dots, u^{2(n-1)}(x)),\quad 0< x< 1,\\ u^{(2i)}(0)= u^{(2i)}(1)= 0,\quad 0\leq i\leq n-1.\end{gathered} \] They develop a monotone iteration method in presence of upper and lower solutions to the above problem. For an earlier result, see \textit{R. Ma}, \textit{J. Zhang} and \textit{S. Fu} [ibid. 215, No. 2, 415-422 (1997; Zbl 0892.34009)].
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34B05
Mathematics Subject Classification ID: 47H10
zbMATH DE Number: 1915761
zbMATH Keywords: Lidstone boundary value problem
zbMATH Keywords: maximum principle
zbMATH Keywords: lower and upper solutions
reviewed by: Ruyun Ma
MaRDI profile type: Publication
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full work available at URL: s0022-247x(03)00011-8
OpenAlex ID: W1988875670
description: scientific article; zbMATH DE number 1915761