Twin positive solutions for higher order m-point boundary value problems with sign changing nonlinearities

A new fixed point theorem on double cones is applied to obtain the existence of at least two positive solutions for the 2nd order m-point boundary value problem y((2n)) (t) = f(t, y(t), y"(t),...,y((2(n- 1))) (t)), 0 less than or equal to t less than or equal to 1, y((2i)) (O) - beta(i)y((2i+1)) (0) = 0, y((2i)) (1) = Sigma(j=1)(m-2)k(ij)y((2i))(xi(j)), 0 less than or equal toi less than or equal to n - 1, where f is allowed to change sign, 0 < xi(1) < xi(2) < (...) < xi(m-2) < 1. The associated Green's function for the above problem is also given. (C) 2002 Elsevier Inc. All rights reserved.