Existence of solutions for third-order boundary value problems on a time scale

Let T be a closed subset of R with inf T = −∞ and sup T = +∞. For the third-order nonlinear equation, uΔ3 = f(t, u, uΔ, uΔΔ), t ε T, where f: T × R3 → R is continous, we assume solutions of initial value problems are unique and extend to T. We consider questions of the uniqueness of solutions implying the existence of solutions for conjugate boundary problems on T.