Copyright © 2010 Wenyong Zhong and Wei Lin. 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.
By virtue of the Avery-Henderson fixed point theorem and the five
functionals fixed point theorem, we analytically establish several sufficient criteria for
the existence of at least two or three positive solutions in the -Laplacian dynamic
equations on time scales with a particular kind of -Laplacian and -point boundary
value condition. It is this kind of boundary value condition that leads the established
criteria to be dependent on the time scales. Also we provide a representative and nontrivial
example to illustrate a possible application of the analytical results established.
We believe that the established analytical results and the example together guarantee
the reliability of numerical computation of those -Laplacian and -point boundary
value problems on time scales.