Matrix systems of differential equations with the quasimonotonicity condition
type: Item
instance of: scholarly article
title: Matrix systems of differential equations with the quasimonotonicity condition
zbMATH Open document ID: 1004.34021
author: A. I. Malikov
published in: Russian Mathematics
publication date: 2000-01-01T00:00:00Z
review text: The author considers initial value problems with quasimonotone increasing right-hand sides in the space of symmetric \(n\times n\)-matrices, ordered by the cone of positive semidefinite matrices. He proves existence of lower and upper solutons, comparison results, monotone dependence on the initial value, and stability, boundedness and invariance results by means of differential inequalities for matrix-valued Lyapunov functions. There seems to be an error in Lemma 4, where it is stated that a quasimonotone increasing function leads to a monotone function by adding a suitable positive multiple of the identity. This does not hold in general, for example, for some of the linear mappings considered in Lemma 10.6.
reviewed by: Gerd Herzog
Mathematics Subject Classification ID: 34C11
Mathematics Subject Classification ID: 34C12
Mathematics Subject Classification ID: 34D20
zbMATH DE Number: 1758686
zbMATH Keywords: quasimonotone functions
zbMATH Keywords: comparison results
zbMATH Keywords: matrix differential equations
zbMATH Keywords: Lyapunov functions
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 1758686