Positive solutions for a system of pp-Laplacian boundary value problems

This paper is concerned with the existence and multiplicity of positive solutions for the system of pp-Laplacian boundary value problems −((ui′)pi−1)′=fi(t,u1,…,un),ui(0)=ui′(1)=0,i=1,…,n, where n⩾2n⩾2, pi>1pi>1, fi∈C([0,1]×R+n,R+)(i=1,…,n,R+:=[0,∞)). Based on a priori estimates achieved by utilizing the Jensen integral inequalities and R+n-monotone matrices, we use fixed point index theory to establish the existence and multiplicity of positive solutions for the above problem.