Advances in Difference Equations
Volume 2005 (2005), Issue 1, Pages 81-92

Periodic boundary value problems on time scales

Petr Stehlík

Department of Mathematics, University of West Bohemia, Univerzitní 22, Plzeň 306 14, Czech Republic

Received 20 April 2004

Copyright © 2005 Petr Stehlík. 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.


We extend the results concerning periodic boundary value problems from the continuous calculus to time scales. First we use the Schauder fixed point theorem and the concept of lower and upper solutions to prove the existence of the solutions and then we investigate a monotone iterative method which could generate some of them. Since this method does not work on each time scale, a condition containing a Lipschitz constant of right-hand side function and the supremum of the graininess function is introduced.