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Non radial positive solutions for the Hénon equation with critical growth

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Abstract.

We study the Dirichlet problem in a ball for the Hénon equation with critical growth and we establish, under some conditions, the existence of a positive, non radial solution. The solution is obtained as a minimizer of the quotient functional associated to the problem restricted to appropriate subspaces of H 0 1 invariant for the action of a subgroup of \({\bf O}(N)\). Analysis of compactness properties of minimizing sequences and careful level estimates are the main ingredients of the proof.

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Authors and Affiliations

  1. Dipartimento di Matematica, Universitá di Milano, Via Saldini 50, 20133 , Milano, Italy

    Enrico Serra

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  1. Enrico Serra
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Correspondence to Enrico Serra.

Additional information

Received: 18 October 2003, Accepted: 5 July 2004, Published online: 3 September 2004

Mathematics Subject Classification (2000):

35J20, 35B33

This research was supported by MIUR, Project "Variational Methods and Nonlinear Differential Equations".

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Serra, E. Non radial positive solutions for the Hénon equation with critical growth. Calc. Var. 23, 301–326 (2005). https://doi.org/10.1007/s00526-004-0302-9

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  • DOI: https://doi.org/10.1007/s00526-004-0302-9

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