Existence of multiple 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′))′+a(t)f(t,u)=0,t∈(0,1) Turn MathJax on View the MathML sourceu(0)=0,u(1)=∑i=1m−2aiu(ξi), Turn MathJax on where ϕp(s)=|s|p−2s,p>1,0<ξ1<ξ2<⋯<ξm−2<1,ai≥0ϕp(s)=|s|p−2s,p>1,0<ξ1<ξ2<⋯<ξm−2<1,ai≥0, for i=1,2,…,m−3i=1,2,…,m−3 and am−2>0am−2>0. 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.