Abstract and Applied Analysis
Volume 2010 (2010), Article ID 307409, 16 pages
doi:10.1155/2010/307409
Research Article

On the Controllability of a Differential Equation with Delayed and Advanced Arguments

Raúl Manzanilla, Luis Gerardo Mármol, and Carmen J. Vanegas

Departamento de Matemáticas Puras y Aplicadas, Universdad Simón Bolívar, Caracas 1080-A, Venezuela

Received 4 January 2010; Revised 26 March 2010; Accepted 20 April 2010

Academic Editor: Roman Šimon Hilscher

Copyright © 2010 Raúl Manzanilla et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

A semigroup theory for a differential equation with delayed and advanced arguments is developed, with a detailed description of the infinitesimal generator. This in turn allows to study the exact controllability of the equation, by rewriting it as a classical Cauchy problem.