Controllability of second-order neutral functional differential inclusions in Banach spaces
type: Item
instance of: scholarly article
title: Controllability of second-order neutral functional differential inclusions in Banach spaces
zbMATH Open document ID: 1025.93006
DOI: 10.1016/S0022-247X(02)00503-6
author: Young Chel Kwun
author: H.-J. Lee
author: Jong Yeoul Park
published in: Journal of Mathematical Analysis and Applications
publication date: 2003-09-25T00:00:00Z
review text: The authors study the controllability of neutral functional differential inclusions in Banach spaces of the form \[ {d\over dt}\{y'(t)-g(t,y_t)\}\in Ay(t)+Bu(t)+F(t,y_t), \quad t\in J:=[0,T], \] \[ y_0=\phi, \quad y'(0)=x_0, \] where \(F: J\times C([-r,0],E)\to 2^E\) is a bounded, closed, convex multivalued map, \(g: J\times C([-r,0],E)\to E\) is a given function, \(\phi \in C([-r,0],E),\) \(x_0\in E,\) \(A\) is the infinitesimal generator of a strongly continuous cosine family \(\{C(t): t\in R\}\) in a real Banach space and the control function \(u(\cdot)\) is given in \(L^2([0,T],U),\) a Banach space of admissible control functions with \(U\) as a Banach space. Finally, \(B\) is a bounded linear operator from \(U\) to \(E.\) The results are obtained by using a fixed point theorem for condensing upper semicontinuous mappings due to Martelli. Reviewer's remark: In (H7) the constant \(M_0\) depends on \(y,\) so in the conclusion of step 5 \(L\) depends also on \(y.\) To avoid this, condition (H7) must be changed to \(\int_{1}^{+\infty}{ds \over s+\Psi(s)}=+\infty\).
Mathematics Subject Classification ID: 93B05
Mathematics Subject Classification ID: 93C23
Mathematics Subject Classification ID: 93C25
Mathematics Subject Classification ID: 34K40
zbMATH DE Number: 1985886
zbMATH Keywords: neutral functional differential inclusions
zbMATH Keywords: controllability
zbMATH Keywords: fixed points
reviewed by: Sotiris K. Ntouyas
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1985886