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International Journal of Mathematics and Mathematical Sciences
Volume 2015, Article ID 828952, 17 pages
http://dx.doi.org/10.1155/2015/828952
Research Article

Periodic Solutions of Certain Differential Equations with Piecewise Constant Argument

Department of Mathematics, SUNY College at Buffalo, 1300 Elmwood Avenue, Buffalo, NY 14222-1095, USA

Received 30 March 2015; Accepted 27 May 2015

Academic Editor: Harvinder S. Sidhu

Copyright © 2015 James Guyker. 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

Existence criteria are derived for the eventually periodic solutions of a class of differential equations with piecewise constant argument whose solutions at consecutive integers satisfy nonlinear recurrence relations. The proof characterizes the initial values of periodic solutions in terms of the coefficients of the resulting difference equations. Sufficient conditions for the unboundedness, boundedness, and symmetry of general solutions also follow from the corresponding properties of the difference equations.