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 = for λ sufficiently small, where is a bounded domain in R^N with smooth boundary ∂Ω and λ is a positive parameter. In this work, we allow the sign changing nature of a and b with a(x)b(x) ≤ 0, ∀x Ie{cyrillic, ukrainian} Ω. © 2011 Texas State University - San Marcos.