Solutions and positive solutions to semipositone Dirichlet bvps on time scales

In this paper, we are concerned with the following Dirichlet boundary value problem on a time scale T [GRAPHICS] where g : [0, T](T) x [-sigma(T) sigma 2(T)M, +infinity) + [-M, +infinity) is continuous and M > 0 is a constant, which implies that this problem is semipositone. For an arbitrary positive integer n, some existence results for n solutions and/or positive solutions are established by using the well-known Guo-Krasnosel'skii fixed point theorem. Our conditions imposed on g are local. An example is also included to illustrate the importance of the results obtained.