TY - JOUR AU - Kajikiya, Ryuji PY - 2015/09/01 Y2 - 2024/03/29 TI - Partially symmetric solutions of the generalized Hénon equation in symmetric domains JF - Topological Methods in Nonlinear Analysis JA - TMNA VL - 46 IS - 1 SE - DO - 10.12775/TMNA.2015.043 UR - https://apcz.umk.pl/TMNA/article/view/TMNA.2015.043 SP - 191 - 221 AB - We study the generalized H\'{e}non 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. ER -