Solution Matching for a Second Order Boundary Value Problem on Time Scales.

Let T be a time scale such that a < b; a, b ∈ 핋. We will show the existence and uniqueness of solutions for the second-order boundary value problem yΔΔ(t) = f(t, y(t), yΔ(t)), t ∈ [a, b]핋, y(a) = A, y(b) = B, by matching a solution of the first equation satisfying boundary conditions on [a, c]핋 with a solution of the first equation satisfying boundary conditions on [c, b]핋, where c ∈ (a, b)핋. [ABSTRACT FROM AUTHOR]