Controllability results for functional semilinear differential inclusions in Fréchet spaces
type: Item
instance of: scholarly article
title: Controllability results for functional semilinear differential inclusions in Fréchet spaces
zbMATH Open document ID: 1086.34062
author: Mouffak Benchohra
author: Abdelghani Ouahab
published in: Nonlinear Analysis. Theory, Methods \& Applications. Series A: Theory and Methods
publication date: 2005-05-12T00:00:00Z
review text: The paper is devoted to four types of inclusions in Fréchet spaces. Namely, first- and second-order semilinear functional-differential inclusions as well as semilinear neutral functional-differen\-tial inclusions. The main goal of the work consists in the proof of theorems on existence and uniqueness of mild solutions to such inclusions. The authors thereto make use of techniques of noncompactness measures, of semigroup theory as well as of one variety of fixed-points theorems -- Frigon's nonlinear alternative. One of the proved theorems is illustrated with a parabolic neutral type partial inclusion. It should be noted that the word ``controllability'' in the paper title has a weak relation to the essence of the issue discussed in the work.
reviewed by: Vyacheslav I. Maksimov
Mathematics Subject Classification ID: 34K30
Mathematics Subject Classification ID: 34K25
Mathematics Subject Classification ID: 34G25
Mathematics Subject Classification ID: 93B05
zbMATH DE Number: 2167866
zbMATH Keywords: differential inclusions
zbMATH Keywords: mild solution
zbMATH Keywords: fixed-point
zbMATH Keywords: Fréchet spaces
zbMATH Keywords: admissible contraction
MaRDI profile type: Publication
full work available at URL: j.na.2004.12.002
OpenAlex ID: W2077567505
cites work: Some Uniqueness Results on Controllability for Functional Semilinear Differential Equations in Fréchet Spaces
cites work: Controllability of nonlinear systems in Banach spaces: a survey
cites work: Controllability results for evolution inclusions with non-local conditions
cites work: Q4658121
cites work: Q5414265
cites work: Q5489552
cites work: An approach to non-linear control problems using fixed-point methods, degree theory and pseudo-inverses.
cites work: Convex analysis and measurable multifunctions
cites work: One-Parameter Semigroups for Linear Evolution Equations
cites work: Q3678037
cites work: Q4793514
cites work: Q3721264
cites work: Condensing multivalued maps and semilinear differential inclusions in Banach spaces
cites work: Semigroups of linear operators and applications to partial differential equations
cites work: Q4520889
cites work: Q3903316
cites work: Cosine families and abstract nonlinear second order differential equations
cites work: Theory and applications of partial functional differential equations
cites work: Q5531981
DOI: 10.1016/J.NA.2004.12.002
description: scientific article; zbMATH DE number 2167866