@article{Castro_Finan_1999, title={Existence of many sign-changing nonradial solutions for semilinear elliptic problems on thin annuli}, volume={13}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.1999.014}, abstractNote={We study the existence of many nonradial sign-changing solutions of a superlinear Dirichlet boundary value problem in an annulus in $\mathbb R^N$. We use Nehari-type variational method and group invariance techniques to prove that the critical points of an action functional on some spaces of invariant functions in $H_{0}^{1,2}(\Omega_{\varepsilon})$, where $\Omega_{\varepsilon}$ is an annulus in $\mathbb R^N$ of width $\varepsilon$, are weak solutions (which in our case are also classical solutions) to our problem. Our result generalizes an earlier result of Castro et al. (See [A. Castro, J. Cossio and J. M. Neuberger, < i> A minmax principle, index of the critical point, and existence of sign-changing solutions to elliptic boundary value problems< /i> , Electron. J. Differential Equations < b> 2< /b> (1998), 1–18]).}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Castro, Alfonso and Finan, Marcel B.}, year={1999}, month={Jun.}, pages={273–279} }