Universite de Chile

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**Abstract**: We consider the following problem

with . We prove that if is fixed, and is close enough to the critical exponent , then there exists a radial solution which behaves like a superposition of bubbles of different blow-up orders centered at the origin. Similarly when is fixed and is sufficiently close to the critic, we prove the existence of a radial solution which resembles a superposition of flat bubbles centered at the origin.