EXISTENCE OF POSITIVE SOLUTIONS TO SEMIPOSITONE DIRICHLET BVPS ON TIME SCALES

In this paper, we are concerned with the following semipositone Dirichlet boundary value problem on a time scale T ( −u ∆∆(t) = g(t, u(t)), t ∈ [0, T]T, u(0) = 0 = u(σ 2 (T)), where g : [0, T]T × [0, +∞) → [−M, +∞) is continuous and M > 0 is a constant. Some existence criteria for at least one positive solution are established by using well-known results from fixed point index theory.