[portuges]babel [latin1]inputenc A PRIORI ESTIMATES AND EXISTENCE OF POSITIVE SOLUTIONS OF NONLINEAR COOPERATIVE ELLIPTIC SYSTEMS

Abstract. We study the existence of positive solutions for elliptic systems of the form (1) below, when f has asymptotic behaviour at + ∞ as uσ and g satisfies some subcritical growth. Our result guarantees a nontrivial solution (u, v) to the system −∆u = uσ + vq,−∆v = up in Ω; u = v = 0 on ∂Ω, where 1 < p, q < pq < σ < (N + 2)/(N − 2). 0. INTRODUCTION histrica In this work our main goal is to obtain positive solutions for the system: −∆u = m11(x)u+m12(x)v + f(x, u, v) in Ω −∆v = m21(x)u+m22(x)v + g(x, u, v) in