In this article, we are concerned with the existence of positive radial solutions of the problem (S+):-Δpu= f(x,u,v) in Ω, -Δqv=g(x,u,v) in Ω, u = v = 0 on partialΩ,where Ω is a ball in RN and f, g are positivefunctions satisfying f(x,0,0)=g(x,0,0)=0. Under some growthconditions, we show the existence of a positive radial solution ofthe problem S+. We use traditional techniques of the topologicaldegree theory. When Ω=RN, we give some sufficientconditions of nonexistence.
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