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 01 invariant for the action of a subgroup. Analysis of compactness properties of minimizing sequences and careful level estimates are the main ingredients of the proof.
Non radial positive solutions for the {H\'enon equation with critical growth / Enrico Serra. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 23:3(2005), pp. 301-326.
Non radial positive solutions for the {H\'enon equation with critical growth
Enrico Serra
2005
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 01 invariant for the action of a subgroup. Analysis of compactness properties of minimizing sequences and careful level estimates are the main ingredients of the proof.
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