Positive solutions for third-order Sturm–Liouville boundary value problems with pp-Laplacian

In this paper, by using the fixed point index method, we establish the existence of at least one or at least two positive solutions for the third-order Sturm–Liouville boundary value problem with pp-Laplacian {(ϕp(u″(t)))′+f(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,p>1. As an application, an example is given to demonstrate the main result.