Existence of positive solutions for boundary-value problems for singular higher-order functional differential equations

Abstract

We study the existence of positive solutions for the boundary-value problem of the singular higher-order functional differential equation

(Ly(n-2))(t) + h(t)ƒ(t, yt) = 0, for t ∈ [0, 1], y(i)(0) = 0, 0 ≤ i ≤ n - 3, ay(n-2)(t) - βy(n-1) (t) = η(t), for t ∈ [-τ, 0], γy(n-2)(t) + δy(n-1) (t) = ξ(t), for t ∈ [1, 1 + α], where Ly := -(py′)′ + qy, p ∈ C([0, 1], (0, +∞)), and q ∈ C([0, 1], [0, +∞)). Our main tool is the fixed point theorem on a cone.