EXISTENCE OF POSITIVE SOLUTIONS FOR SEMILINEAR ELLIPTIC SYSTEMS WITH INDEFINITE WEIGHT

This article concerns the existence of positive solutions of semilinear elliptic 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 subset of R-N (N >= 1) is a bounded domain with a smooth boundary partial derivative Omega and lambda is a positive parameter. a, b : Omega -> R are sign-changing functions. f, g : [0, infinity) -> R are continuous with f(0) > 0, g(0) > 0. By applying Leray-Schauder fixed point theorem, we establish the existence of positive solutions for lambda sufficiently small.