Positive solutions for one-dimensional pp-Laplacian boundary value problems with sign changing nonlinearity

This paper deals with the existence of positive solutions for the one-dimensional pp-Laplacian (ϕp(u′))′+f(t,u,u′)=0,t∈[0,1], subject to the boundary value conditions: u′(0)=∑i=1nαiu′(ξi),u(1)=∑i=1nβiu(ξi), where ϕp(s)=|s|p−2s,p>1ϕp(s)=|s|p−2s,p>1. We show that it has at least one or two positive solutions under some assumptions by applying the fixed point theorem. The interesting points are that the nonlinear term ff is involved with the first-order derivative explicitly and ff may change sign.