Positive solutions for second-order quasilinear multi-point boundary value problems

In this paper a new fixed point theorem in a cone is applied to obtain the existence of at least one positive solution for second-order quasilinear m-point boundary value problem(ϕp(x′(t)))′+a(t)f(t,x,x′)=0,0⩽t⩽1,x′(0)=0,x(1)=∑i=1m-2αix(ξi),where f   is a nonnegative continuous function and ϕp(x)=∣x∣p-2x,p>1ϕp(x)=∣x∣p-2x,p>1. A simple example is presented to illustrate the applications of the obtained results.