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On the spectrum of general second order operators. (English) Zbl 0141.09901

MSC:
35P15 Estimates of eigenvalues in context of PDEs
35B50 Maximum principles in context of PDEs
Citations:
JFM 63.0762.02
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References:
[1] J. Barta, Sur la vibration fondamentale d’une membrane, C. R. Acad. Sci. Paris 204 (1937), 472-473. · JFM 63.0762.02
[2] R. J. Duffin, Lower bounds for eigenvalues, Physical Rev. (2) 71 (1947), 827 – 828.
[3] Joseph Hersch, Sur la fréquence fondamentale d’une membrane vibrante: évaluations par défaut et principe de maximum, Z. Angew. Math. Phys. 11 (1960), 387 – 413 (French, with English summary). · Zbl 0104.41403
[4] W. W. Hooker, Lower bounds for the first eigenvalue of elliptic equations of orders two and four, Tech. Rep. 10, AF49(638)-398, Univ. of California, Berkeley, California, 1960.
[5] M. G. Kreĭn and M. A. Rutman, Linear operators leaving invariant a cone in a Banach space, Uspehi Matem. Nauk (N. S.) 3 (1948), no. 1(23), 3 – 95 (Russian). · Zbl 0030.12902
[6] M. H. Protter, Lower bounds for the first eigenvalue of elliptic equations, Ann. of Math. (2) 71 (1960), 423 – 444. · Zbl 0095.20004
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