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

Let T be a closed subset of R with inf T = ∞ and sup T = +∞. For the fourth order nonlinear dynamic equation, u[SUPΔ4] = f (t, u, u[SUPδ u[SUPδ2], u[SUPΔ3]). t ∊ T; where f : T × R[SUP4] → 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. [ABSTRACT FROM AUTHOR]