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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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