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Concentrating solutions for the Hénon equation in ℝ2

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Abstract

We consider the boundary value problem Δu+⋎x⋎2α 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.

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Authors and Affiliations

  1. Dipartimento di Matematica, Università degli Studi “Roma Tre”, Largo S. Leonardo Murialdo, 1-00146, Roma, Italy

    Pierpaolo Esposito

  2. Pacific Institute for the Mathematical Sciences, University of British Columbia, 1933 West Mall, V6T 1Z2, Vancouver, BC, Canada

    Pierpaolo Esposito

  3. Dipartimento di Metodi e Modelli Matematici, Università di Roma “La Sapienza”, Via Scarpa, 16-00166, Roma, Italy

    Angela Pistoia

  4. Department of Mathematics, Chinese University of Hong Kong, Shatin, N.T., Hong Kong

    Juncheng Wei

Authors
  1. Pierpaolo Esposito
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  2. Angela Pistoia
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  3. Juncheng Wei
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Corresponding author

Correspondence to Pierpaolo Esposito.

Additional information

The first author is supported by M.U.R.S.T., project “Variational methods and nonlinear differential equations” and a PIMS Postdoctoral Fellowship.

The second author is supported by M.U.R.S.T., project “Metodi variazionali e topologici nello studio di fenomeni non lineari.”

The third author is supported by an Earmarked Grant from RGC of HK.

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Esposito, P., Pistoia, A. & Wei, J. Concentrating solutions for the Hénon equation in ℝ2 . J. Anal. Math. 100, 249–280 (2006). https://doi.org/10.1007/BF02916763

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  • DOI: https://doi.org/10.1007/BF02916763

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