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Encadrement du N($$\lambda$$ ) pour un opérateur de Schrödinger avec un champ magnétique et un potentiel électrique. (Inclusion of N($$\lambda$$ ) for a Schrödinger operator with magnetic field and electric potential). (French) Zbl 0725.35068
The authors study the asymptotic behaviour at infinity of the number N($$\lambda$$) of the eigenvalues in ]-$$\infty,\lambda]$$ of the Schrödinger operator with magnetic field $$H=\sum^{n}_{j=1}(- i\partial_{x_ j}-a_ j(x))^ 2+V(x)$$. Under regularity and increasing assumptions on V and the $$a_ j's$$, they obtain upper and lower bounds for N($$\lambda$$). These bounds are integrals of some quantities associated to V and the $$a_ j's$$. Several examples are given where V and the $$a_ j's$$ are polynomials.

##### MSC:
 35P20 Asymptotic distributions of eigenvalues in context of PDEs 35J10 Schrödinger operator, Schrödinger equation
magnetic field