We study the generalized Hénon equation in a symmetric domain $\Omega$. Let $H$ and $G$ be closed subgroups of the orthogonal group such that $H \varsubsetneq G$ and $\Omega$ is $G$ invariant. Then we show the existence of a positive solution which is $H$ invariant but $G$ non-invariant under suitable assumptions of $H,G$ and the coefficient function of the equation.
"Partially symmetric solutions of the generalized Hénon equation in symmetric domains." Topol. Methods Nonlinear Anal. 46 (1) 191 - 221, 2015. https://doi.org/10.12775/TMNA.2015.043