Monotone method for a system of second order periodic boundary value problems
type: Item
instance of: scholarly article
title: Monotone method for a system of second order periodic boundary value problems
zbMATH Open document ID: 0541.34009
DOI: 10.1016/0096-3003(84)90054-7
author: V. Sree Hari Rao
author: V. Lakshmikantham
author: Aghalaya S. Vatsala
published in: Applied Mathematics and Computation
publication date: 1984-01-01T00:00:00Z
review text: The paper considers the periodic boundary value problem \((*)\quad - u''\!_ i=f_ i(t,u,u'\!_ i),\quad u(0)=u(2\pi),\quad u'(0)=u'(2\pi),\) where \(f\in C([0,2\pi]\times R^ n\times R,R^ n)\) (1\(\leq i\leq n)\). Given two non-negative integers \(p_ i\) and \(q_ i\) such that \(p_ i+q_ i=n-1,\) the vector u is split up as \(u=(u_ i,U_{p_ i},U_{q_ i})\), picking out the \(u_ i\) component. Then the coupled periodic quasi-solutions u, v associated with (*) are defined as satisfying \(-u''\!_ i=f_ i(t,u_ i,U_{p_ i},V_{q_ i},u'\!_ i),\quad -v''\!_ i=f_ i(t,v_ i,V_{p_ i},U_{q_ i},v'\!_ i)\) as well as having period 2\(\pi\). Subject to various conditions on f, it is shown that there are monotonic sequences of solutions of the corresponding differential inequalities which converge to coupled minimal and maximal periodic quasi-solutions. The uniqueness of the solutions of (*) is also investigated.
Mathematics Subject Classification ID: 34B15
zbMATH DE Number: 3859527
zbMATH Keywords: differential inequalities
zbMATH Keywords: maximal periodic quasi-solutions
MaRDI profile type: Publication
full work available at URL: 0096-3003(84)90054-7
OpenAlex ID: W1969100104
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description: scientific article; zbMATH DE number 3859527