Three positive solutions for multipoint one-dimensional p-Laplacian boundary value problems with dependence on the first order derivative

By applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions for the one-dimensional p-Laplacian differential equation, (ϕp(u′(t)))′+q(t)f(t,u(t),u′(t))=0,t∈(0,1), subject to the following multipoint boundary condition, u′(0)=∑i=1nαiu′(ξi),u(1)=∑i=1nβiu(ξi), where ϕp(s)=|s|p−2sϕp(s)=|s|p−2s with p>1p>1. The interesting point is the nonlinear term ff is involved with the first-order derivative explicitly.