# Concentrating solutions for the Hénon equation in ℝ^{2}

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DOI: 10.1007/BF02916763

- Cite this article as:
- Esposito, P., Pistoia, A. & Wei, J. J. Anal. Math. (2006) 100: 249. doi:10.1007/BF02916763

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## Abstract

We consider the boundary value problem Δ*u*+⋎*x*⋎^{2α}*u*^{p}=0, α>0, in the unit ball*B* with homogeneous Dirichlet boundary condition and*p* a large exponent. We find a condition which ensures the existence of a positive solution*u*_{p} concentrating outside the origin at*k* symmetric points as*p* 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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© Hebrew University 2006