Abstract and Applied Analysis
Volume 2012 (2012), Article ID 851691, 25 pages
http://dx.doi.org/10.1155/2012/851691
Research Article

Study of Solutions to Some Functional Differential Equations with Piecewise Constant Arguments

Juan J. Nieto1,2 and Rosana Rodríguez-López1

1Departamento de Análisis Matemático, Facultad de Matemáticas, Universidad de Santiago de Compostela, 15782 Santiago de Compostela, Spain
2Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O. Box 80203, Jeddah 21589, Saudi Arabia

Received 12 October 2011; Revised 6 January 2012; Accepted 9 January 2012

Academic Editor: Josef Diblík

Copyright © 2012 Juan J. Nieto and Rosana Rodríguez-López. 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

We provide optimal conditions for the existence and uniqueness of solutions to a nonlocal boundary value problem for a class of linear homogeneous second-order functional differential equations with piecewise constant arguments. The nonlocal boundary conditions include terms of the state function and the derivative of the state function. A similar nonhomogeneous problem is also discussed.