Advances in Difference Equations 
Volume 2006 (2006), Article ID 73860, 12 pages
doi:10.1155/ADE/2006/73860

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

Abstract

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.