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 O(N). Analysis of compactness properties of minimizing sequences and careful level estimates are the main ingredients of the proof.

Non radial positive solutions for the Henon equation with critical growth / Serra, Enrico. - In: CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS. - ISSN 0944-2669. - 23:(2005), pp. 301-326.

### Non radial positive solutions for the Henon equation with critical growth

#### 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 O(N). Analysis of compactness properties of minimizing sequences and careful level estimates are the main ingredients of the proof.
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Utilizza questo identificativo per citare o creare un link a questo documento: `https://hdl.handle.net/11583/1719271`