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 ∈ (0, 1), −v = g(t,u), t ∈ (0, 1), u(0) = v(0) = 0, αu(η)= u(1), αv(η) = 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. © 2005 Published by Elsevier Inc.