Multiple positive solutions for boundary value problems of second order delay differential equations with one-dimensional p-Laplacian

We consider the boundary value problems: (ϕp(x′′(t)))+q(t)f(t,x(t),x(t−1),x′(t))=0, ϕp(s)=|s|p−2s, p>1, t∈(0,1), subject to some boundary conditions. By using a generalization of the Leggett–Williams fixed-point theorem due to Avery and Peterson, we provide sufficient conditions for the existence of at least three positive solutions to the above problems.