Positive solutions for multipoint boundary value problems with a one-dimensional image-Laplacian Original Research Article

In this paper we consider the multipoint boundary value problem for a one-dimensional pp-Laplacian: View the MathML source(ϕp(u′))′+f(t,u)=0,t∈(0,1) Turn MathJax on subject to the boundary value condition: View the MathML sourceu′(0)=∑i=1n−2αiu′(ξi),u(1)=∑i=1n−2βiu(ξi), Turn MathJax on where ϕp(s)=|s|p−2s,p>1,ξi∈(0,1)ϕp(s)=|s|p−2s,p>1,ξi∈(0,1) with 0<ξ1<ξ2<⋯<ξn−2<10<ξ1<ξ2<⋯<ξn−2<1, and αi,βiαi,βi satisfy αi,βi∈[0,∞)αi,βi∈[0,∞), View the MathML source0<∑i=1n−2αi<1, and View the MathML source∑i=1n−2βi<1. Using a fixed point theorem for operators on a cone, we provide sufficient conditions for the existence of multiple positive solutions to the above boundary value problem.