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An identity for elliptic equations with applications


Author: C. A. Swanson
Journal: Trans. Amer. Math. Soc. 134 (1968), 325-333
MSC: Primary 35.11
DOI: https://doi.org/10.1090/S0002-9947-1968-0232074-1
MathSciNet review: 0232074
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  • [1] K. O. Friedrichs, Spektraltheorie halbbeschränkter Operatoren und Anwendung auf die Spektralzerlegung von Differentialoperatoren, Math. Ann. 109 (1934), 465-487. MR 1512905
  • [2] F. R. Gantmacher, The theory of matrices, Vol. I, Chelsea, New York, 1959.
  • [3] I. M. Glazman, Direct methods of qualitative spectral analysis of singular differential operators, Israel Program for Scientific Translations, Davey, New York, 1965. MR 0190800 (32:8210)
  • [4] Philip Hartman and Aurel Wintner, On a comparison theorem for self-adjoint partial differential equations of elliptic type, Proc. Amer. Math. Soc. 6 (1955), 862-865. MR 0074668 (17:627b)
  • [5] Teruo Ikebe and Tosio Kato, Uniqueness of the self-adjoint extension of singular elliptic differential operators, Arch. Rational Mech. Anal. 9 (1962), 77-92. MR 0142894 (26:461)
  • [6] Kurt Kreith, Oscillation theorems for elliptic equations, Proc. Amer. Math. Soc. 15 (1964), 341-344. MR 0197939 (33:6098)
  • [7] Walter Leighton, The detection of the oscillation of solutions of a second order linear differential equation, Duke Math. J. 17 (1950), 57-62; On self-adjoint differential equations of second order, J. London Math. Soc. 27 (1952), 37-47. MR 0032065 (11:248c)
  • [8] M. H. Protter, A comparison theorem for elliptic equations, Proc. Amer. Math. Soc. 10 (1959), 296-299. MR 0107076 (21:5803)
  • [9] -, Lower bounds for the first eigenvalue of elliptic equations, Ann. of Math. 71 (1960), 423-444. MR 0111923 (22:2781)
  • [10] M. H. Protter and H. F. Weinberger, On the spectrum of general second order operators, Bull. Amer. Math. Soc. 72 (1966), 251-255. MR 0190527 (32:7939)
  • [11] C. A. Swanson, A comparison theorem for elliptic differential equations, Proc. Amer. Math. Soc. 17 (1966), 611-616. MR 0201781 (34:1663)
  • [12] -, Comparison theorems for elliptic equations on unbounded domains, Trans. Amer. Math. Soc. 126 (1967), 278-285. MR 0203211 (34:3064)
  • [13] Aurel Wintner, A criterion of oscillatory stability, Quart. Appl. Math. 7 (1949), 115-117. MR 0028499 (10:456a)

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DOI: https://doi.org/10.1090/S0002-9947-1968-0232074-1
Article copyright: © Copyright 1968 American Mathematical Society

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