@article{Grossi_Pacella_Yadava_2003, title={Symmetry results for perturbed problems and related questions}, volume={21}, url={https://apcz.umk.pl/TMNA/article/view/TMNA.2003.013}, abstractNote={In this paper we prove a symmetry result for positive solutions of the Dirichlet problem
$$
\cases
-\Delta u=f(u) & \hbox{in }D,\\
u=0 & \hbox{on }\partial D, \endcases
\tag{0.1}
$$
when $f$ satisfies suitable assumptions and $D$ is a small symmetric perturbation of a domain $\Omega$
for which the Gidas-Ni-Nirenberg symmetry theorem applies.
We consider both the case when $f$ has subcritical growth and $f(s)=s^{(N+2)/(N-2)}+\lambda s$,
$N\ge3$, $\lambda$ suitable positive constant.}, number={2}, journal={Topological Methods in Nonlinear Analysis}, author={Grossi, Massimo and Pacella, Filomena and Yadava, S. L.}, year={2003}, month={Jun.}, pages={211–226} }