Existence results for initial value problems for neutral functional differential inclusions in Banach spaces
type: Item
instance of: scholarly article
title: Existence results for initial value problems for neutral functional differential inclusions in Banach spaces
zbMATH Open document ID: 1160.34070
author: B. E. Eshmatov
published in: Acta Mathematica Vietnamica
publication date: 2008-10-20T00:00:00Z
review text: The author proves an existence result for the following initial value problem \[ \frac{d}{dx}[x(t)-g(t,x_{t})] \in F(t,x_{t}), \enskip t\in I, \] \[ x_0=\phi, \] where \(\phi \in C([-r,0],E)\), \(r>0\), \(E\) is a Banach space, \(I=[0,\omega]\), \(g:I\times C([-r,0],E)\to E\) is a continuous function and \(F\) an appropriate multimapping. The proof is based on an application of the topological transversality for multimappings. An application of the main result is also given for the optimal control of a system described by an integrodifferential equation.
reviewed by: Panagiotis Ch. Tsamatos
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 35K40
Mathematics Subject Classification ID: 35K05
zbMATH DE Number: 5354275
zbMATH Keywords: neutral functional differential inclusions in Banach spaces
zbMATH Keywords: initial value problem existence results
zbMATH Keywords: topological transversality
zbMATH Keywords: \(\chi\)-Lipschitz multimappings
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 5354275