Infinitely many non-radial solutions to a critical equation on annulus (Q1671218)

The paper deals with the critical elliptic problem \[ \begin{cases} -\Delta u=|u|^{\frac{4}{N-2}}u,\,\,\,\text{in}\,\,\,\Omega,\\ u=0,\,\,\,\text{on}\,\,\,\partial \Omega, \end{cases}\leqno{(1)} \] where \(\Omega=\{x\in\mathbb{R}^N,\,\,a<|x|<b\}\) is an annulus, and \(N\geq 3\). Under the assumption that the unique positive radial solution \(u_0\) of problem (1) is non-degenerate, and by using a Lyapunov-Schmidt procedure, the authors prove the existence of infinitely many non-radial sign-changing solutions of (1) which are invariant under the action of a group whose orbits are finite.