The existence of positive solutions for some nonlinear equation systems

In this paper we consider the existence of positive solutions of the following boundary value problem:{(φ1(x′))′+a(t)f(x,y)=0,(φ2(y′))′+b(t)g(x,y)=0,t∈(0,1),αφ1(x(0))−βφ1(x′(0))=0,αφ2(y(0))−βφ2(y′(0))=0,γφ1(x(1))+μφ1(x′(1))=0,γφ2(y(1))+μφ2(y′(1))=0, where φ1,φ2:R→R are the increasing homeomorphism and positive homomorphism and φ1(0)=0φ1(0)=0, φ2(0)=0φ2(0)=0. We show the sufficient conditions for the existence of positive solutions by using the nome type cone expansion–expression fixed point theorem.