## Advances in Differential Equations

### Bifurcation and symmetry breaking for the Henon equation

#### Abstract

In this paper, we consider the problem $$\left\{ \begin{array}{ll} -\Delta u=|x|^{\alpha}u^p & \text{ in } B ,\\ u>0 & \hbox{ in } B ,\\ u=0 & \hbox{ on }\partial B , \end{array}\right.$$ where $B$ is the unit ball of $\mathbb R^N$, $N\ge 3$, $p > 1$ and $0 < \alpha\leq 1$. We prove the existence of (at least) one branch of non-radial solutions that bifurcate from the radial ones and that this branch is unbounded.

#### Article information

Source
Adv. Differential Equations Volume 19, Number 7/8 (2014), 755-782.

Dates
First available in Project Euclid: 6 May 2014

Permanent link to this document
https://projecteuclid.org/euclid.ade/1399395725

Mathematical Reviews number (MathSciNet)
MR3252901

Zentralblatt MATH identifier
1320.35056

#### Citation

Amadori, Anna Lisa; Gladiali, Francesca. Bifurcation and symmetry breaking for the Henon equation. Adv. Differential Equations 19 (2014), no. 7/8, 755--782. https://projecteuclid.org/euclid.ade/1399395725.