In this paper, we prove a global bifurcation result for the existence of non-radial branches of solutions to the paramterized family of $\Gamma$-symmetric problems $-\Delta u=f(\alpha,z,u)$, $u|_{ \partial D}=0$ on the unit disc $D:=\{ z\in \mathbb{ C} : |z|<1\}$ with $u(z)\in \mathbb{ R}^k$, where $\mathbb{ R}^k$ is an orthogonal $\Gamma$-representation, $f: \mathbb{ R} \times \overline{ D} \times \mathbb{ R}^k\to \mathbb{ R}^k$ is a sub-linear $\Gamma$-equivariant continuous function, differentiable with respect to $u$ at zero and satisfying the conditions $f(\alpha, e^{ i\theta}z,u)=f(\alpha, z,u)$ for all $\theta\in \mathbb{ R}$ and $f(z,-u)=-f(z,u)$.
Categories: math.AP