Several sufficient conditions of solvability for a nonlinear higher-order three-point boundary value problem with all derivatives

In this paper, firstly, some errors in the proof of our paper “Several sufficient conditions of solvability for a nonlinear higher-order three-point boundary value problem on time scales, Appl. Math. Comput. 190 (2007) 566-575” are pointed, and we make the corresponding correction when T=R. Then, the more general problem with all derivatives is considered. Under certain growth conditions on the nonlinearity, several sufficient conditions for the existence and uniqueness of nontrivial solution are obtained by using Leray-Schauder nonlinear alternative and Banach fixed point theorem.