Positive solutions of m-point boundary value problems for higher order ordinary differential equations

摘要

In this paper, we study m-point boundary value problems for higher order ordinary differential equation y((2n)) (t) = f (t, y(t), y ''(t),...,y((2(n-1)) (t)), 0 <= t <= 1, y((2i)) (0) = 0, y((2i)) (1) = Sigma(m-2)(j=1) k(ij)y((2i)) (xi(j)) 0 <= i <= n - 1, where f is allowed to change sign, and 0 = xi(0) < xi(1) < xi(2) < ,..., < xi(m-2) < xi(m-1) = 1. We show sufficient conditions for the existence of at least two positive solutions by applying a new fixed point theorem in cones and the associated Green's function. In particular, the second positive solutions for the above problem is not concave. (c) 2006 Elsevier Ltd. All rights reserved.