Coupled solutions and monotone iterative techniques for some nonlinear initial value problems on time scales.
type: Item
instance of: scholarly article
title: Coupled solutions and monotone iterative techniques for some nonlinear initial value problems on time scales.
zbMATH Open document ID: 1037.34003
DOI: 10.1016/S1468-1218(02)00008-1
author: Billûr Kaymakçalan
author: Bonita A. Lawrence
published in: Nonlinear Analysis. Real World Applications
publication date: 2003-05-14T00:00:00Z
review text: The authors present the monotone iterative technique for nonlinear initial value problems, which consists in approximating the unique solution by lower and upper solutions. The well-known theory is generalized in two respects: 1) Various types of (dynamic) inequalities (with natural or coupled solutions) constitute the framework of the theory. 2) The set of the underlying independent variable, which is \(\mathbb R\) in the classical theory, is replaced by a general time scale, i.e., an arbitrary closed subset of \(\mathbb R\). So, also the difference equations case (\(\mathbb Z\) as a time scale) is covered. The authors also point out applications to the logistic equation of mathematical biology. Reviewer's remark: An error in step (iii) of the proof of Theorem 3.3 can be fixed.
reviewed by: Stefan Hilger
Mathematics Subject Classification ID: 34A12
Mathematics Subject Classification ID: 39A10
zbMATH DE Number: 1910217
zbMATH Keywords: monotone iterative technique
zbMATH Keywords: time scales
zbMATH Keywords: logistic equation
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1910217