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) = 0, ϕ2(0) = 0. We show the sufficient conditions for the existence of positive solutions by using the nome type cone expansion–expression fixed point theorem. © 2005 Elsevier Inc. All rights reserved