Three positive solutions for higher order m-point boundary value problems

In this paper, we consider the existence of at least three positive solutions for the 2nth order m-point boundary value problem y((2n))(t) = f(t,y(t),y"(t),...,y((2(n+1)))(t)), 0less than or equal totless than or equal to1, [GRAPHICS] where k(ij)>0 (i=0,1,...,n-1; j=1,2,...,m-2), 0<xi(1)<xi(2)<center dot center dot center dot<xi(m-2)<1. The associated Green's function for the higher order m-point boundary value problem is first given, and growth conditions are imposed on f which yield the existence of multiple positive solutions by using the Leggett-Williams fixed point theorem. (C) 2003 Elsevier Inc. All rights reserved.