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: (psi(1)(x'))' + a(t)f(x,y) = 0, (psi(2)(y'))' + b(t)g(x,y) = 0, t is an element of (0,1), { alpha psi(1)(x(0)) - beta psi(1)(x'(0)) = 0, alpha psi(2)(y(0)) - beta psi(2)(y'(0)) = 0, gamma psi(1)(x(1)) + mu psi(1)(x'(1)) = 0, gamma alpha(2)(y(1)) + mu psi(2)(y'(1)) = 0, where psi 1, psi 2: R -> R are the increasing homeomorphism and positive homomorphism and psi 1(0) = 0, psi 2(0) = 0. We show the sufficient conditions for the existence of positive solutions by using the nome type cone expansion-expression fixed point theorem. (c) 2005 Elsevier Inc. All rights reserved.