Existence of Solutions for Fourth Order Boundary Value Problems on a Time Scale

Let T be a closed subset of R with inf T =-infinity and sup T =+infinity. For the fourth order nonlinear dynamic equation, u(Delta4) = f (t , u , u(Delta) , u(Delta2) , u(Delta3)), t is an element of T , where f : T x R-4 --> R is continuous, 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 .