Comparison principle based on Minkowski mixed volumes for a family of differential equations
type: Item
instance of: scholarly article
title: Comparison principle based on Minkowski mixed volumes for a family of differential equations
zbMATH Open document ID: 1393.34031
DOI: 10.1134/S0012266117120035
published in: Differential Equations
publication date: 2018-04-06T00:00:00Z
review text: The paper studies a family of differential equations of the form \[ D_HX=F(t,X,\alpha ),\quad X(t_0)=X_0\in K_c({\mathbb R}^n), \] where \(D_H\) is the generalized (Hukuhara) derivative, \(K_c({\mathbb R}^n)\) denotes the space of nonempty compact convex subsets of \({\mathbb R}^n\), \(\alpha \) is the imprecision parameter varying in a compact set \({\mathcal J}\subset {\mathbb R}^d\) and \(F(.,.,.):{\mathbb R}_+\times K_c({\mathbb R}^n)\times {\mathcal J}\to K_c({\mathbb R}^n)\) is continuous. Under certain hypotheses two comparison principles concerning Minkowski mixed volumes are obtained for the problem considered.
reviewed by: Aurelian Cernea
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C10
zbMATH DE Number: 6856618
zbMATH Keywords: Hukuhara derivative
zbMATH Keywords: Minkowski mixed volumes
zbMATH Keywords: convex body
author: A. A. Martynyuk
MaRDI profile type: Publication
cites work: Q2935988
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full work available at URL: s0012266117120035
OpenAlex ID: W2791689790
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description: scientific article; zbMATH DE number 6856618