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

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.


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


[1] DOI: 10.1090/pspum/065/1662746
[2] DOI: 10.1002/cpa.3160360405 · Zbl 0541.35029
[3] DOI: 10.1142/S0218127400001006 · Zbl 1090.65549
[4] DOI: 10.1016/0022-0396(84)90153-0 · Zbl 0569.35033
[5] DOI: 10.1007/BF00282336 · Zbl 0616.35029
[6] DOI: 10.1007/BF01221125 · Zbl 0425.35020
[7] Hénon M., Astronomy and Astrophysics 24 pp 229– (1973)
[8] DOI: 10.3934/dcds.2000.6.683 · Zbl 1157.35342
[9] DOI: 10.1512/iumj.1982.31.31056 · Zbl 0515.35033
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.