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