Positive solutions for nonlinear m-point boundary value problems of Dirichlet type via fixed-point index theory

Let a is an element of C[0, 1], b is an element of C([0, 1], (-infinity, 0)). Let phi(1)(t) be the unique solution of the linear boundary value problem u"(t) + a(t)u'(t) + b(t)u(t) = 0, t is an element of (0, 1), u(0) = 0, u(1) = 1. We study the multiplicity of positive solutions for the m-point boundary value problems of Dirichlet type u" + a(t)u' + b(t)u + g(t) f (u) = 0, u(0) = 0, u(1) - Sigma(i=1)(m-2) alpha(i)u(xi(i)) = 0, where xi(i) is an element of (0, 1) and alpha(i) is an element of (0, infinity), i is an element of {1,..., m-2}, are given constants satisfying Sigma(i=1)(m-2) alpha(i)phi(1)(xi(i)) < 1. The methods employed are fixed-point index theory. (C) 2003 Elsevier Science Ltd. All rights reserved.