Asymptotic bounds on the number of the eigenvalues in the gaps of the 2D magnetic Schrödinger operator

We consider the two‐dimensional Schrödinger operator with generically bounded magnetic field, perturbed by a scalar potential $-gV$ , $g \geq 0$ being the coupling constant. We assume that $V$ is non‐negative and decays rapidly at infinity (e.g., $V({\mathbf x})\asymp \vert{\mathbf x}\vert^{-\alpha}$ , $\alpha > 2$ , as $\vert{\mathbf x}\vert\rightarrow \infty$ ). We examine the asymptotic behaviour as $g \rightarrow \infty$ of the eigenvalues situated in the gaps of the spectrum of the unperturbed operator.