Advances in Difference Equations 
Volume 2006 (2006), Article ID 79689, 18 pages
doi:10.1155/ADE/2006/79689

Boundedness in functional dynamic equations on time scales

Elvan Akin-Bohner1 and Youssef N. Raffoul2

 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

Abstract

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.