Non-radial ground states for the Hénon equation. (English) Zbl 1160.35415

Smets, Didier; Willem, Michel; Su, Jiabao

Commun. Contemp. Math. 4, No. 3, 467-480 (2002).

The authors’ deal with Hénon’s equation, that is \[ \begin{gathered} -\Delta u= |x|^\alpha u^{p-1},\;u> 0\quad\text{in }B_1,\\ u= 0\quad\text{on }\partial B_1,\end{gathered}\tag{1} \] where \(B_1= \{x\in\mathbb{R}^N\mid\| x\|\leq 1\}\). They are mainly interested in the symmetry of ground state solutions of (1). They present asymptotic estimates of the transition, when \(p\) is close to either 2 or \(2^*= {2N\over N-22}\), \(N\geq 3\). Moreover, they present some numerical computations concerning the transition from radialicity to symmetry breaking and a breaking and a generalization to the \(q\)-Laplacian as well.

Reviewer: Messoud A. Efendiev (Berlin)

MSC:

35J60	Nonlinear elliptic equations
35J20	Variational methods for second-order elliptic equations
35J25	Boundary value problems for second-order elliptic equations

Keywords:

Hénon equation; ground state solution; symmetry breaking

References:

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