Asymptotics and estimates of the discrete spectrum of the Schrodinger operator on a discrete periodic graph

Abstract

The periodic Schrodinger operator $H$ on a discrete periodic graph is considered. We estimate the discrete spectrum of the perturbed operator $H_{-}(t)=H-tV$, $t>0$, where the potential $Vge0$ is decreasing and $t>0$ is the coupling constant. If the potential has a power asymptotics at infinity, then we obtain asymptotics of the discrete spectrum of operator $H_{-}(t)$ with a large coupling constant.

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