Existence and uniqueness of solutions to first-order three-point boundary value problems Original Research Article

We give the existence and uniqueness results of solutions for the three-point boundary value problems where f : [a, c] × Rn → Rn satisfies Carathéodoryʹs conditions, and M, N, and R are constant square matrices of order n and α ϵ Rn. The existence of a solutions is proven by the Leray-Schauder continuation theorem.