Solvability of a multi-point boundary value problem of Neumann type

Abstract

Let f:[0,1]×?2?? be a function satisfying Carathéodory's conditions and e(t)?L1[0,1]. Let ?i?(0,1),ai??,i=1,2,…,m?2,0<?1<?2<?<?m?2<1 be given. This paper is concerned with the problem of existence of a solution for the m-point boundary value problem x?(t)=f(t,x(t),x?(t))