Abstract : In this article we present several results of spectrum analysis, the most part of which based on the min-max variational principle. The main goal here is to prove some Weyl-type formula for some kinds of Schrodinger operators . The Weyl asymptotics are a basic result in semi-classical analysis, they relate the number of eigenvalues to the volume in phase space of the trajectories for the associated classical dynamics. We consider operators for which that volume is infinite, so that the Weyl formula has to be revisited. We also present a problem of magnetic bottle in classical dynamics, which is at the origin of the questions discussed in the semi-classical context.