EXISTENCE OF NON-NEGATIVE SOLUTIONS FOR PREDATOR-PREY ELLIPTIC SYSTEMS WITH A SIGN-CHANGING NONLINEARITY

By the method of monotone iteration and Schauder fixed point theorem, we prove the existence of non-negative solutions to the system -Delta u = lambda a(x)f(v) in Omega, -Delta v = lambda b(x)g(u) in Omega, u = v = 0 on partial derivative Omega, for lambda sufficiently small, where Omega is a bounded domain in R-N with smooth boundary partial derivative Omega and lambda is a positive parameter. In this work, we allow the sign changing nature of a and b with a(x)b(x) <= 0, for all x is an element of (Omega) over bar.