Multiple positive solutions for image-point boundary-value problems with a one-dimensional image-Laplacian Original Research Article

In this paper, we consider the multipoint boundary- value problem for the one-dimensional pp-Laplacian View the MathML source(ϕp(u′))′+q(t)f(t,u)=0,t∈(0,1), Turn MathJax on subject to the boundary conditions: View the MathML sourceu(0)=∑i=1m−2aiu(ξi),u(1)=∑i=1m−2biu(ξi), Turn MathJax on where ϕp(s)=|s|p−2sϕp(s)=|s|p−2s. By using a fixed point theorem in a cone, we present sufficient conditions for the existence of multiple positive solutions for the above boundary value problem.