The relation between the first and second natural frequencies of vibrations of a membrane
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 2, pp. 320-325 Cet article a éte moissonné depuis la source Math-Net.Ru

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A. S. Bratus'; A. D. Myshkis. The relation between the first and second natural frequencies of vibrations of a membrane. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 32 (1992) no. 2, pp. 320-325. http://geodesic.mathdoc.fr/item/ZVMMF_1992_32_2_a11/

[1] Paynel L. E., Polya G., Weinberger H. F., “On the ratio of consecutive eigenvalues”, J. Math. Phys., 35 (1956), 289–298 | MR

[2] Brands J. J., “Bounds for the ratios of the first three membrane eigenvalues”, Arch. Ration. Mech. and Analys., 16 (1964), 265–268 | DOI | MR | Zbl

[3] Bile G. N., Protter M. H., “Inequalities for eigenvalues of laplacian”, Indiana Univ. Math. J., 29:4 (1980), 523–538 | DOI | MR

[4] Protter M. H., “Can one hear the shape of a drum”, SIAM Rev., 29:2 (1987), 185–197 | DOI | MR | Zbl

[5] De Vries N. L., “On the upper bound for the ratio of the first two membrane eigenvalues”, Z. Naturforschung., 22a (1987), 152–153 | MR

[6] Arnold V. I., Vishik M. I., Ilyashenko Yu. S. i dr., “Nekotorye nereshennye zadachi teorii differentsialnykh uravnenii i matematicheskoi fiziki”, Uspekhi matem. nauk, 44:4(268) (1989), 191–202 | MR

[7] Bratus A. S., Myshkis A. D., “Usloviya ekstremuma v spektralnykh izoperimetricheskikh zadachakh s izmenyayuscheisya granitsei”, Zh. vychisl. matem. i matem. fiz., 27:12 (1987), 1790–1801 | MR