Positive solutions of three-point boundary value problems for systems of nonlinear second order ordinary differential equations

In this paper, we study the three-point boundary value problems for systems of nonlinear second order ordinary differential equations of the form -u" = f(t, v), t is an element of (0, 1), -v" = g(t, u), t is an element of (0, 1), u(0) = v(0) = 0, alpha u(eta) = u(1), alpha v(eta) = v(1). Under some conditions, we show the existence and multiplicity of positive solutions of the above problem by applying the fixed point index theory in cones. (C) 2005 Published by Elsevier Inc.