Non radial positive solution for the Hénon equation with critical growth. (English) Zbl 1207.35147

Serra, Enrico

Calc. Var. Partial Differ. Equ. 23, No. 3, 301-326 (2005).

Summary: 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.

MSC:

35J60	Nonlinear elliptic equations
35J20	Variational methods for second-order elliptic equations
35B33	Critical exponents in context of PDEs

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