Riccati differential inequalities and dichotomies for linear systems
type: Item
instance of: scholarly article
title: Riccati differential inequalities and dichotomies for linear systems
zbMATH Open document ID: 1017.34055
DOI: 10.1016/S0022-247X(02)00111-7
author: James S. Muldowney
author: Marcos Lizana
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-11-28T00:00:00Z
review text: Here, the authors consider finite-dimensional ordinary differential equations \(x'=A(t)x\), where \(A(t)\) is continuous, and provide criteria for them to possess a so-called \((\mu_1,\mu_2)\)-dichotomy. This dichotomy notion was introduced by the second author in [Trans. Am. Math. Soc. 283, 465--484 (1984; Zbl 0559.34049)] and includes ordinary and exponential dichotomies as special cases. The mentioned dichotomy criteria assume the existence of certain solutions to a Riccati differential inequality. In fact, the use of these Riccati inequalities leads to results extending earlier conditions expressed in terms of pairs of Lyapunov functions, and makes them easier to apply. Moreover, it provides a relaxation of the concept of diagonal dominance. Finally, as an application of their results, the authors give a proof for the roughness of \((\mu_1,\mu_2)\)-dichotomies.
Mathematics Subject Classification ID: 34D09
Mathematics Subject Classification ID: 34A30
zbMATH DE Number: 1836756
zbMATH Keywords: dichotomy
zbMATH Keywords: linear systems of differential equations
reviewed by: Christian Pötzsche
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1836756