Advances in Difference Equations
Volume 2006 (2006), Article ID 73860, 12 pages
On lower and upper solutions without ordering on time scales
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.