Advances in Difference Equations
Volume 2006 (2006), Article ID 73860, 12 pages

On lower and upper solutions without ordering on time scales

Petr Stehlík

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

Received 31 January 2006; Revised 16 May 2006; Accepted 16 May 2006

Copyright © 2006 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.


In order to enlarge the set of boundary value problems on time scales, for which we can use the lower and upper solutions technique to get existence of solutions, we extend this method to the case when the pair lacks ordering. We use the degree theory and a priori estimates to obtain the existence of solutions for the second-order Dirichlet boundary value problems. To illustrate a wider application of this result, we conclude with an example which shows that a combination of well and non-well ordered pairs can yield the existence of multiple solutions.