On a discreteness condition of the spectrum of Schrödinger operators with unbounded potential from below

On a discreteness condition of the spectrum of Schrödinger operators with unbounded potential from below
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by V. Benci and D. Fortunato PDF

Proc. Amer. Math. Soc. 70 (1978), 163-166 Request permission

We obtain a discreteness condition for the spectrum of the Schrödinger operator $- \Delta + V(x)$ in a case in which V is not bounded from below.

References

V. Benci and D. Fortunato, Discreteness conditions of the spectrum of Schrödinger operators, J. Math. Anal. Appl. 64 (1978), no. 3, 695–700. MR 481616, DOI 10.1016/0022-247X(78)90013-6
V. Benci and D. Fortunato, Some compact embedding theorems for weighted Sobolev spaces, Boll. Un. Mat. Ital. B (5) 13 (1976), no. 3, 832–843 (English, with Italian summary). MR 0435825
Melvyn S. Berger and Martin Schechter, Embedding theorems and quasi-linear elliptic boundary value problems for unbounded domains, Trans. Amer. Math. Soc. 172 (1972), 261–278. MR 312241, DOI 10.1090/S0002-9947-1972-0312241-X
I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Israel Program for Scientific Translations, Jerusalem, 1965; Daniel Davey & Co., Inc., New York, 1966. Translated from the Russian by the IPST staff. MR 0190800

Ob usloviayakh discretinosti spekra samosopryazhennykh differentsial’nykh uravnenji vtorogo poryadka

The conditions for the discreteness of the spectrum of selfadjoint second-order differential equations

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Martin Schechter, Spectra of partial differential operators, 2nd ed., North-Holland Series in Applied Mathematics and Mechanics, vol. 14, North-Holland Publishing Co., Amsterdam, 1986. MR 869254
Barry Simon, Quantum mechanics for Hamiltonians defined as quadratic forms, Princeton Series in Physics, Princeton University Press, Princeton, N. J., 1971. MR 0455975
Guido Stampacchia, Le problème de Dirichlet pour les équations elliptiques du second ordre à coefficients discontinus, Ann. Inst. Fourier (Grenoble) 15 (1965), no. fasc. 1, 189–258 (French). MR 192177, DOI 10.5802/aif.204