Article

Journal d’Analyse Mathématique

, Volume 100, Issue 1, pp 249-280

First online:

Concentrating solutions for the Hénon equation in ℝ2

  • Pierpaolo EspositoAffiliated withDipartimento di Matematica, Università degli Studi “Roma Tre”Pacific Institute for the Mathematical Sciences, University of British Columbia Email author 
  • , Angela PistoiaAffiliated withDipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”
  • , Juncheng WeiAffiliated withDepartment of Mathematics, Chinese University of Hong Kong

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Abstract

We consider the boundary value problem Δu+⋎x u p =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 solutionu p 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.