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

Let be a time scale such that <;,∈. We will show the existence and uniqueness of solutions for the second-order boundary value problem ΔΔ()=(,(),Δ()),∈[,],()=,()=, by matching a solution of the first equation satisfying boundary conditions on [,] with a solution of the first equation satisfying boundary conditions on [,], where ∈(,).