Concentrating solutions for the Hénon equation in ℝ2
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We consider the boundary value problem Δu+⋎x⋎2αup=0, α>0, in the unit ballB with homogeneous Dirichlet boundary condition andp a large exponent. We find a condition which ensures the existence of a positive solutionup concentrating outside the origin atk symmetric points asp goes to +∞. The same techniques lead also to a more general result on general domains. In particular, we find that concentration at the origin is always possible, provided α⊄IN.
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