We study global properties of positive radial solutions of $ -\Delta u = u^p+M\left |{\nabla u}\right |^{\frac{2p}{p+1}} $ in $ \mathbb R^N $ where $ p>1 $ and $ M $ is a real number. We prove the existence or the non-existence of ground states and of solutions with singularity at $ 0 $ according to the values of $ M $ and $ p $.
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