Existence theorems for a second order m-point boundary value problem

Let f:[0, 1] x R-2 --> R be continuous and e is an element of C[0, 1]. Let xi(i) is an element of (0, 1), a(i) is an element of R, all of the a(i)'s having the same sign, i = 1, 2,..., m - 2, 0 < xi(1) < xi(2) < ... < xi(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)) + e(t), t is an element of (0, 1) (E) x'(0) = 0, x(1) = (i=1)Sigma(m-2) a(i)x(xi(i)). (BCm) We discuss existence theorems for the problem (E)-(BCm) under some sign condition of f about the origin. Our analysis is based on a Nonlinear Alternative of Leray-Schauder. (C) 1997 Academic Press.