Existence of nonnegative solutions for a class of semilinear elliptic systems with indefinite weight

We prove the existence of nonnegative solutions to the system -Delta u = lambda a(x)f(v) in Omega, -Delta v = lambda b(x)g(u) in Omega, u = 0 =v on partial derivative Omega, where Omega is a bounded domain in R(N) with a smooth boundary partial derivative Omega, lambda is a positive parameter. By the method of monotone iteration and Schauder fixed point theorem, we prove the existence of a nonnegative solution to the above system for lambda sufficiently small. In this study, we do not restrict the sign of a and b. (C) 2010 Elsevier Ltd. All rights reserved.