On positive solutions of boundary value problems for second-order functional differential equations on infinite intervals

We study the existence of positive solutions for the following boundary value problem on infinite interval for second-order functional differential equations:  x (t )−px (t )− qx(t) + f (t,xt ) = 0, t∈ [0,∞), αx(t)− βx (t ) = ξ(t), t ∈ [−τ, 0], limt→∞x(t) = 0, and  x (t )−px (t )− qx(t) + f (t,xt,x t ) = 0, t∈ [0,∞), αx(t)− βx (t ) = ξ(t), t ∈ [−τ, 0], limt→∞x(t) = 0, where p,α,β 0, α2 +β2 > 0, and q >0. The fixed point theorem on cone is used.  2003 Elsevier Inc. All rights reserved