Copyright © 2009 You-Hui Su and Can-Yun Huang. 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.
This paper makes a study on the existence of positive solution to -Laplacian dynamic
equations on time scales . Some new sufficient conditions are obtained for the existence of at least single or twin positive solutions by using Krasnosel'skii's fixed point theorem and new sufficient conditions are also obtained for the existence of at least triple or arbitrary odd number positive solutions by using generalized Avery-Henderson fixed point theorem and Avery-Peterson fixed point theorem. As applications,
two examples are given to illustrate the main results and their differences. These results are even new for the special cases of continuous and discrete equations, as well as in the general time-scale setting.