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.