Spèctre négatif d'un opérateur elliptique avec des conditions au bords de Robin

In this article we discuss some estimates of the number of the negative eigenvalues and their moments of energy for an elliptic operator $L=L_0-V(x)$ defined in $H^m(\mathbb{R}^n_+)$ with the Robin boundary conditions containing a potential $W(x)$, in terms of some integrals of $V$ and $W$.