Existence and iteration of positive solutions for third-order Sturm–Liouville boundary value problems with p-Laplacian

In this paper, we investigate the existence and iteration of positive solutions for the following third-order Sturm–Liouville boundary value problem with p-Laplacian {(ϕp(u′′(t)))′+q(t)f(t,u(t),u′′(t))=0,t∈(0,1),αu(0)−βu′(0)=0,γu(1)+δu′(1)=0,u′′(0)=0,where ϕp(s)=|s|p−2s,ϕp(s)=|s|p−2s,p > 1. By applying a monotone iterative technique, we not only obtain the existence of positive solutions for the above boundary value problem, but also establish iterative schemes for approximating the solutions.