Triple positive solutions of mm-point BVPs for pp-Laplacian dynamic equations on time scales

This paper is concerned with the existence of positive solutions of pp-Laplacian dynamic equation (φp(uΔ(t)))∇+a1(t)f(u(t))=0(φp(uΔ(t)))∇+a1(t)f(u(t))=0 subject to boundary conditions View the MathML sourceu(0)−B0(∑i=1m−2aiuΔ(ξi))=0,uΔ(T)=0 or View the MathML sourceuΔ(0)=0,u(T)+B1(∑i=1m−2biuΔ(ξi))=0, where φp(v)=|v|p−2vφp(v)=|v|p−2v with p>1p>1. By using the five functionals fixed-point theorem, we prove that the boundary value problem has at least three positive solutions. As an application, an example is given to illustrate the result.