Existence of solutions of nonlinear m-point boundary-value problems

We study the existence of positive solutions to the boundary-value problem u " + a(t)f(u) = 0, t is an element of (0, 1) x'(0)= Sigma (m-2)(i=1) b(i)x'(xi (i)), x(1) = Sigma (m-2)(i=1) a(i)x(xi (i )), where xi (i) is an element of (0, 1) with 0 < <xi>(1) < <xi>(2) < <xi>(m-2) < 1, a(i), b(i) <is an element of> [0, infinity) with 0 < <Sigma>(m-2)(i=1 ) a(i) < 1, and <Sigma>(m-2)(i=1) b(i) < 1. We show the existence of at lea st one positive soIution if f is either superlinear or sublinear by applyin g the fixed point theorem in cones. <(c)> 2001 Academic Press.