Copyright © 2009 Wei Han and Shugui Kang. 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 using fixed point theorems in cones, the
existence of multiple positive solutions is
considered for nonlinear -point boundary
value problem for the following second-order boundary value problem on time scales
, , , ,
where is an increasing homeomorphism and homomorphism
and . Some new results are obtained for the existence of twin or an arbitrary odd number of positive solutions of the above problem by applying Avery-Henderson and Leggett-Williams fixed point theorems, respectively. In particular, our criteria generalize and
improve some known results by Ma and Castaneda (2001). We must point out for readers that there is only the -Laplacian case for increasing homeomorphism and homomorphism. As an application, one example to demonstrate our results is given.