# Nondegeneracy of positive solutions to nonlinear Hardy-Sobolev equations

1 EDP - Equations aux dérivées partielles IECL - Institut Élie Cartan de Lorraine

Abstract : In this note, we prove that the kernel of the linearized equation around a positive energy solution in $\mathbb{R}^n$, $n\geq 3$, to $-\Delta W-\gamma|x|^{-2}V=|x|^{-s}W^{2^\stars-1}$ is one-dimensional when $s+\gamma>0$. Here, $s\in 0,2$, \$0\leq\gamma

Author: Frédéric Robert -

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