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

Abstract

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