Optimal existence conditions for the periodic delay \(\phi\)-Laplace equation with upper and lower solutions in the reverse order
type: Item
instance of: scholarly article
title: Optimal existence conditions for the periodic delay \(\phi\)-Laplace equation with upper and lower solutions in the reverse order
zbMATH Open document ID: 1059.34049
DOI: 10.1007/BF03322992
author: Wenjie Zuo
author: Daqing Jiang
author: Donal O'Regan
author: Ravi P. Agarwal
published in: Results in Mathematics
publication date: 2004-05-27T00:00:00Z
review text: This paper deals with the scalar periodic delay \(\phi\)-Laplace equation \[ -\frac{d}{dt}\phi(u'(t))=f(t,u(t),u(t-\tau)),\quad t\in\mathbb{R},\tag{1} \] where \(f: \mathbb{R}^3\to \mathbb{R}\) is a continuous function and \(f(t,u,v)=f(t+\tau,u,v)\), \(\tau>0\); \(\phi:\mathbb{R}\to \mathbb{R}\) is an increasing homeomorphism such that \(\phi(0)=0\). The authors show that the monotone iterative technique generates two monotone sequences that converge uniformly to extremal solutions of (1). Moreover, the authors obtain optimal existence conditions with upper and lower solutions in the reverse order.
reviewed by: Jurang Yan
Mathematics Subject Classification ID: 34K13
Mathematics Subject Classification ID: 34K10
zbMATH DE Number: 2067314
zbMATH Keywords: periodic solution
zbMATH Keywords: upper and lower solutions
zbMATH Keywords: monotone iterative technique
zbMATH Keywords: extremal solution
MaRDI profile type: Publication
cites work: Q3807603
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description: scientific article; zbMATH DE number 2067314