Solvability of singular second order m-point boundary value problems

Let f:[0,1]×R2→R be a function satisfying Carathéodory's conditions and (1−t)e(t)∈L1(0,1). Let ξi∈(0,1), ai∈R, i=1,…,m−2, 0<ξ1<ξ2<⋯<ξm−2<1 be given. This paper is concerned with the problem of existence of a C1[0,1) solution for the m-point boundary value problem x″=f(t,x(t),x′(t))+e(t),0