Symmetry breaking of an elliptic equation in expanding annuli

We obtain non-radial bifurcation from radial solutions of a semilinear elliptic equation in expanding annuli of \(\mathbb {R}^N\). To obtain the main results, we use a blow-up argument via the Morse index of the regular entire solutions of the equation

$$\begin{aligned} -\Delta u=\lambda u^p \quad \text {in}\quad \mathbb {R}^N. \end{aligned}$$

(0.1)

The main results of this paper can be seen as applications of the properties of regular entire solutions of (0.1).