# Some Liouville theorems for Hénon type elliptic equations

1 Département de Mathématiques Cergy-Pontoise 2 EDP - Equations aux dérivées partielles IECL - Institut Élie Cartan de Lorraine

Abstract : We investigate here the nonlinear elliptic equations$-\Delta u = |x|^{\alpha} e^{u}$ and $-\Delta u=|x|^{\alpha}|u|^{p-1}u$ with $\alpha>-2$, $p > 1$ and $N \geq 2$.In particular, we prove some Liouville type theorems for weaksolutions with finite Morse index in the low dimensional Euclideanspaces or half spaces.

Keywords : 35B45 finite Morse index solution MSC: 35J60 Liouville theorem Hénon equation stability

Author: Chao Wang - Dong Ye -

Source: https://hal.archives-ouvertes.fr/