Nonlinear evolution equations without convexity
type: Item
instance of: scholarly article
title: Nonlinear evolution equations without convexity
zbMATH Open document ID: 0835.34022
author: Francesca Papalini
published in: Journal of Mathematical Analysis and Applications
publication date: 1996-04-15T00:00:00Z
review text: The purpose of this article is to prove an existence result for the Cauchy problem \(x' \in - \partial^- f(x) + F(x)\), \(x(0) = x_0\), \(x_0 \in D (\partial^- f)\), where \(f : \Omega \subset \mathbb{R}^n \to \mathbb{R} \cup \{+ \infty\}\) is a function with \(\psi\)-monotone subdifferential of order 2 such that the mapping \(x \mapsto \text{grad}^- f(x)\) is locally bounded in \(x_0\) and \(F : U(x_0) \to 2^{\mathbb{R}^n}\) is an upper semicontinuous and cyclically monotone multivalued operator defined on some neighborhood of \(x_0\) and with nonempty compact values. This theorem extends a previous result of \textit{A. Cellina} and \textit{V. Staicu} [J. Differ. Equations 90, 71-80 (1991; Zbl 0719.34030)] and strictly contains a theorem due to \textit{A. Bressan}, \textit{A. Cellina} and \textit{G. Colombo} [Proc. Am. Math. Soc. 106, 771-775 (1989; Zbl 0698.34014)] for the problem \(x' \in F(x)\), \(x(0) = x_0\).
reviewed by: Adrian Petruşel
Mathematics Subject Classification ID: 34A60
Mathematics Subject Classification ID: 34G20
zbMATH DE Number: 811180
zbMATH Keywords: function with \(\psi\)-monotone
zbMATH Keywords: subdifferential of order 2
zbMATH Keywords: existence
zbMATH Keywords: Cauchy problem
zbMATH Keywords: cyclically monotone multivalued operator
MaRDI profile type: Publication
full work available at URL: jmaa.1995.1243
OpenAlex ID: W2095363130
DOI: 10.1006/JMAA.1995.1243
description: scientific article; zbMATH DE number 811180