Positive solutions for one-dimensional image-Laplacian boundary value problems with sign changing nonlinearity Original Research Article

This paper deals with the existence of positive solutions for the one-dimensional pp-Laplacian View the MathML source(ϕp(u′))′+f(t,u,u′)=0,t∈[0,1], Turn MathJax on subject to the boundary value conditions: View the MathML sourceu′(0)=∑i=1nαiu′(ξi),u(1)=∑i=1nβiu(ξi), Turn MathJax on 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.