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The lower spectrum of Schrödinger operators. (English) Zbl 0455.35046

MSC:
35J10 Schrödinger operator, Schrödinger equation
35P05 General topics in linear spectral theory for PDEs
35P15 Estimates of eigenvalues in context of PDEs
Citations:
Zbl 0381.35026
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References:
[1] Allegretto, W., On the equivalence of two types of oscillation for elliptic operators. Pacific J. Math. 55, 319–328 (1974). · Zbl 0279.35036
[2] Deift, P. A., Applications of a commutation formula. Duke Math. J. 45, 267–310 (1978). · Zbl 0392.47013
[3] Gilbarg, D., & N. S. Trudinger, Elliptic partial differential equations of second order. Berlin, Heidelberg, New York: Springer 1977. · Zbl 0361.35003
[4] Glazman, I. M., Direct methods of qualitative spectral analysis of singular differential operators. Jerusalem: Israel program for scientific translations 1965.
[5] Hartman, P., Ordinary differential equations. New York: Wiley 1964. · Zbl 0125.32102
[6] Kalf, H., A characterization of the Friedrichs extension of Sturm-Liouville operators. J. London Math. Soc. 17, 511–521 (1978). · Zbl 0406.34029
[7] Moss, W. F., & J. Piepenbrink, Positive solutions of elliptic equations. Pacific J. Math. 75, 219–226 (1978). · Zbl 0381.35026
[8] Piepenbrink, J., Finiteness of the lower spectrum of Schrödinger operators. Math. Z. 140, 29–40 (1974) · Zbl 0305.35076
[9] Reed, M., & B. Simon, Methods of modern mathematical physics IV: Analysis of operators. New York, San Francisco, London: Academic Press 1978. · Zbl 0401.47001
[10] Schmincke, U.-W., On Schrödinger’s factorization method for Sturm-Liouville operators. Proc. Royal Soc. Edinburgh Sect. A 80, 67–84 (1978). · Zbl 0395.47022
[11] Simader, C. G., Essential self-adjointness of Schrödinger operators bounded from below. Math. Z. 159, 47–50 (1978). · Zbl 0409.35026
[12] Simon, B., The bound state of weakly coupled Schrödinger operators in one and two dimensions. Ann. Phys. 97, 279–288 (1976). · Zbl 0325.35029
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