Minimal solutions of multivalued differential equations
type: Item
instance of: scholarly article
title: Minimal solutions of multivalued differential equations
zbMATH Open document ID: 0733.34024
author: Dieter Bothe
published in: Differential and Integral Equations
publication date: 1991-01-01T00:00:00Z
review text: Consider \(u'\in F(t,u)\), \(u(0)=x_ 0\) with F: [0,a]\(\times {\mathbb{R}}^ n\to 2^{{\mathbb{R}}^ n}\setminus \emptyset\). Let K be an arbitrary cone in \({\mathbb{R}}^ n\) with nonempty interior and assume that there is f(t,x) such that \(f(t,x)\in (t,x)\subset f(t,x)+K\), where f is quasimonotone in x. Among other conditions, F is assumed to be almost lsc. The author is able to prove that there is an increasing sequence of continuous functions converging pointwise to f, and then to prove that the problem has a minimal solution. The merit of the paper lies in the arbitrariness of the cone K.
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34C11
zbMATH DE Number: 4212490
zbMATH Keywords: partial order
zbMATH Keywords: multivalued functions
zbMATH Keywords: cone
zbMATH Keywords: minimal solution
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 4212490