Conditions for semi-boundedness and discreteness of the spectrum to Schrödinger operator and some nonlinear PDEs

Leonid Zelenko

For Schrödinger operator $H=-\Delta +V(\mathbf{x})\cdot$, acting in the space $L_2({\mathbb{R}}^d)(d\ge 3)$, necessary and sufficient conditions for semi-boundedness and discreteness of…