Advances in Difference Equations
Volume 2006 (2006), Article ID 79689, 18 pages
Boundedness in functional dynamic equations on time scales
1Department of Mathematics and Statistics, University of Missouri-Rolla, 310 Rolla Building, Rolla 65409-0020, MO, USA
2Department of Mathematics, University of Dayton, Dayton 45469-2316, OH, USA
Received 1 February 2006; Revised 25 March 2006; Accepted 27 March 2006
Copyright © 2006 Elvan Akin-Bohner and Youssef N. Raffoul. 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.
Using nonnegative definite Lyapunov functionals, we prove general
theorems for the boundedness of all solutions of a functional
dynamic equation on time scales. We apply our obtained results to
linear and nonlinear Volterra integro-dynamic equations on time
scales by displaying suitable Lyapunov functionals.