Open Access

Periodic boundary value problems on time scales

Advances in Difference Equations20052005:141356

DOI: 10.1155/ADE.2005.81

Received: 20 April 2004

Published: 14 March 2005

Abstract

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.

Authors’ Affiliations

(1)
Department of Mathematics, University of West Bohemia

Copyright

© Stehlík 2005