Positive solutions for semilinear elliptic systems with sign-changing potentials

In this paper, we study the existence of positive solutions of the Dirichlet problem -Delta u = lambda p(x)f(u,v); -Delta v = lambda q(x)g(u,v), in D, and u = v = 0 on partial derivative(infinity) D, where D subset of R-n (n >= 3) is an C-1,C-1-domain with compact boundary and lambda > 0. The potential functions p, q are not necessarily bounded, may change sign and the functions f, g : R-2 -> R are continuous with f(0, 0) > 0, g(0, 0) > 0. By applying the Leray-Schauder fixed point theorem, we establish the existence of positive solutions for lambda sufficiently small.