The Open Automation and Control Systems Journal

2009, 2 : 1-7
Published online 2009 March 13. DOI: 10.2174/1874444300902010001
Publisher ID: TOAUTOCJ-2-1

Controllability of Damped Second Order Semi-linear Neutral Functional Differential Inclusions in Banach Spaces

Dimplekumar N. Chalishajar
213 Carpenter Hall, Department of Mathematics, Mary Baldwin College, Staunton, VA-24401, USA or Mallory Hall, Virginia Military Institute (VMI), Lexington, VA- 24450, USA.

ABSTRACT

In this article, we investigate sufficient conditions for controllability of second-order semi-linear damped 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 Benchohra, Gorniewicz and Ntouyas [1] and extends the work of Chalishajar [2].

Keywords:

Controllability, initial value problems, convex multi-valued map.