ON A FIRST-ORDER SEMIPOSITONE BOUNDARY VALUE PROBLEM ON A TIME SCALE

We consider the existence of a positive solution to the first-order dynamic equation y(Delta)(t)+p(t)y(sigma)(t) = lambda f (t, y(sigma) (t)), t is an element of (a, b)(T), subject to the boundary condition y(a) = y(b) + integral(T2)(T1) F(s, y(s)) Delta s for T-1, T-2 is an element of [a, b](T). In this setting, we allow f to take negative values for some (t, y). Our results generalize some recent results for this class of problems, and because we treat the problem on a general time scale T we provide new results for this problem in the case of differential, difference, and q-difference equations. We also provide some discussion of the applicability of our results.