Existence of positive solutions for higher-order functional differential equations

Under suitable conditions on f (t,y(t+θ)), the boundary value problem of higher-order functional differential equation (FDE) of the form (BVP)   (FDE) y(n)(t )+ f (t,y(t + θ)) = 0, t∈ [0, 1], θ ∈ [−τ,a], (BC)   y(i)(0) = 0, 0 i n −3, αy(n−2)(t )− βy(n−1)(t )= η(t), t ∈ [−τ, 0], γy(n−2)(t )+ δy(n−1)(t ) = ξ(t), t ∈ [1, 1 + a], has at least one positive solution, where θ ∈ [−τ,a] is a fixed constant. Moreover, we also apply this main result to establish several existence theorems which guarantee (BVP) has multiple positive solutions.  2003 Elsevier Inc. All rights reserved