SOLVABILITY OF AN M-POINT BOUNDARY-VALUE PROBLEM FOR 2ND-ORDER ORDINARY DIFFERENTIAL-EQUATIONS

Let f: [0, 1] x R(2) --> R be a function satisfying Caratheodory's conditions and e(t) is an element of L(1) [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 (E) x''(t) = f(t, x(t), x'(t)) + e(t), t is an element of (0, 1), [GRAPHICS] Conditions for the existence of a solution for the above boundary value problem are given using the Leray-Schauder continuation theorem. (C) 1995 Academic Press, Inc.