Extremal solutions of second order nonlinear periodic boundary value problems
type: Item
instance of: scholarly article
title: Extremal solutions of second order nonlinear periodic boundary value problems
zbMATH Open document ID: 0723.65056
DOI: 10.1016/0096-3003(90)90128-P
published in: Applied Mathematics and Computation
publication date: 1990-01-01T00:00:00Z
review text: The authors consider the periodic boundary value problems of the form \(- u''(t)=f(t,u(t),u'(t)),\text{ for } a.e.\quad t\in [0,2\pi],\quad u(0)=u(2\pi),\) where f is a Carathéodory function. They develop a monotone method to obtain the existence of extremal solutions between the lower and upper solutions as uniform limit of monotone sequences. This result is a generalization of results earlier obtained by the second author to the case of functions f depending also on \(u'\).
Mathematics Subject Classification ID: 65L10
Mathematics Subject Classification ID: 34B15
Mathematics Subject Classification ID: 34C15
zbMATH DE Number: 4192984
zbMATH Keywords: monotone iterative method
zbMATH Keywords: periodic boundary value problems
zbMATH Keywords: extremal solutions
zbMATH Keywords: lower and upper solutions
author: Alberto Cabada
author: Juan J. Nieto
MaRDI profile type: Publication
Wikidata QID: Q60199491
cites work: An introduction to nonlinear boundary value problems
cites work: Q4748596
cites work: A generalization of the monotone iterative technique for nonlinear second order periodic boundary value problems
cites work: Q3807603
cites work: A monotone method for constructing extremal solutions of second order scalar boundary value problems
cites work: Q5734753
description: scientific article; zbMATH DE number 4192984