Positive solutions for a functional delay second-order three-point boundary-value problem

Abstract

We establish criteria for the existence of positive solutions to the three-point boundary-value problems expressed by second-order functional delay differential equations of the form -x″(t) = ƒ(t, x(t), x(t - τ), xt), 0 < t < 1, x0 = ϕ, x(1) = x(η), where ϕ ∈ C[-τ, 0], 0 < τ < 1/4, and τ < η < 1.