Triple positive solutions for a class of boundary value problems for second-order neutral functional differential equations

We obtain sufficient conditions for the existence of at least three positive solutions for the second-order neutral functional differential equation x″(t)+q(t)f(t,x(t),x(t−τ),x′(t),x′(t−τ))=0,00, subject to one of the following two pairs of boundary conditions: {x(t)=ξ(t),−τ≤t≤0,x(1)=0{x(t)=ξ(t),−τ≤t≤0,x′(1)=0 and generalize and correct some conditions of Theorem 3.2 in [X.B. Shu, Y.T. Xu, Triple positive solutions for a class of boundary value problems of second-order functional differential equations, Nonlinear Anal. 61 (8) (2005) 1401–1411]. This is an application of a new fixed-point theorem introduced by Avery and Peeterson [R.I. Avery, A.C. Peeterson, Three positive fixed points of nonlinear operators on ordered Banach spaces, Comput. Math. Appl. 42 (2001) 313–322].