First approximation stability theorems for differential inclusions.
type: Item
instance of: scholarly article
title: First approximation stability theorems for differential inclusions.
zbMATH Open document ID: 1083.34039
DOI: 10.1023/B:MATN.0000043478.69896.74
author: V. S. Klimov
published in: Mathematical Notes
publication date: 2005-06-21T00:00:00Z
review text: A family of a multi-valued mapping \(A_{\rho}:R_{+}\times V\to V^{*}\) is introduced by \[ A_{\rho}(t,v) = A(t,v) + \rho\| v\| B_{V^{*}}, \] where \(\rho \geq 0, t\geq 0, v\in V, B_{V^{*}}=\{v^{*}\in V^{*}, \| v^{*}\| _{*} \leq 1\},\) \(V\) is a reflexive separable \(B\)-space with norm \(\| \cdot\|\) and \(V^{*}\) is its dual space with norm \(\| \cdot\| _{*}.\) Suppose that the multi-valued mapping \(A\) satisfies some conditions and that the zero solution of the inclusion \( 0\in y' + A(t,y) \) is exponentially stable in the small. Then there is a \(\rho_{0}>0\) such that, for \(\rho\in (0,\rho_{0}),\) the trivial solution of the inclusion \( 0\in y' + A_{\rho}(t,y)\) is also exponentially stable in the small.
Mathematics Subject Classification ID: 34D20
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 2177659
zbMATH Keywords: differential inclusion
zbMATH Keywords: stability theorem
zbMATH Keywords: approximation
zbMATH Keywords: Banach space
MaRDI profile type: Publication
full work available at URL: b:matn.0000043478.69896.74
OpenAlex ID: W2088295934
description: scientific article; zbMATH DE number 2177659