George, Raju K.; Chalishajar, Dimplekumar N.; Nandakumaran, Akambadath K. Controllability of second order semi-linear neutral functional differential inclusions in Banach spaces. (English) Zbl 1167.93316 Mediterr. J. Math. 1, No. 4, 463-477 (2004). Summary: In this article, we investigate sufficient conditions for controllability of a second order semi-linear neutral functional initial value problem for the class of differential inclusions in Banach spaces using the theory of strongly continuous cosine families. We shall rely on a fixed point theorem due to Ma for multi-valued maps. An example is provided to illustrate the result. This work is motivated by the paper of M. Benchohra, L. Górniewicz and S. K. Ntouyas [Discuss. Math., Differ. Incl. Control Optim. 21, No. 2, 261–282 (2001; Zbl 1020.93004)]. Cited in 4 Documents MSC: 93B05 Controllability 93C10 Nonlinear systems in control theory 49J24 Optimal control problems with differential inclusions (existence) (MSC2000) 47H10 Fixed-point theorems Keywords:controllability; initial value problems; convex multi-valued map; evolution inclusion; fixed point Citations:Zbl 1020.93004 PDFBibTeX XMLCite \textit{R. K. George} et al., Mediterr. J. Math. 1, No. 4, 463--477 (2004; Zbl 1167.93316) Full Text: DOI