Differential inequalities for hysteresis systems
type: Item
instance of: scholarly article
title: Differential inequalities for hysteresis systems
zbMATH Open document ID: 0873.34009
DOI: 10.1155/S1048953396000408
author: Vladimir V. Chernorutskii
author: M. A. Krasnosel'skij
published in: Journal of Applied Mathematics and Stochastic Analysis
publication date: 1997-11-06T00:00:00Z
full work available at URL: https://eudml.org/doc/47713
review text: Let \(W\) denote the so-called deterministic transducer i.e. a dynamical system having inputs and outputs. Denote by \(\Omega(W)\) the state space of the transducer \(W\) and let \({\mathcal F}(F)\) stand for the image of the set \(\Omega(W)\) with respect to the mapping \(F\). The object of the paper is the study of the functional-differential equation (1) \(x'(t)= f(t,x(t),\xi(t))\) with the initial values (2) \(x(t_0)=x_0\), \(w_0(t_0)= w_0\in\Omega(W)\). Here \(x(t)\in \mathbb{R}^n\), \(f:\mathbb{R}\times \mathbb{R}^n\times {\mathcal F}(F)\to\mathbb{R}^n\) is a continuous function and \(\xi(t)\) is an output of the hysteresis nonlinearity \(W\) corresponding to the input \(x(t)\). With help of the concept of semiorder of the state space \(\Omega(W)\) and the concept of monotonicity a few results concerning differential inequalities associated to the problem (1)--(2) are derived. The existence of minimal and maximal solutions of the problem also proved.
Mathematics Subject Classification ID: 34A40
Mathematics Subject Classification ID: 47H30
Mathematics Subject Classification ID: 37-XX
zbMATH DE Number: 988084
zbMATH Keywords: dynamical system
zbMATH Keywords: functional-differential equation
zbMATH Keywords: hysteresis nonlinearity
zbMATH Keywords: differential inequalities
reviewed by: Józef Banaś
MaRDI profile type: Publication
OpenAlex ID: W2130286434
description: scientific article; zbMATH DE number 988084