Geodesic
Asymptotics of eigenvalues of fourth order differential operator with alternating weight function
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2018), pp. 46-58
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We study a fourth-order differential operator with a sign-alternating weight function with separated boundary conditions. For large values of the spectral parameter the asymptotics of the solutions to the corresponding differential equations is derived. The study of boundary conditions makes it possible to obtain an equation for eigenvalues of the considered differential operator. The indicator diagram of this equation is studied. The asymptotics of eigenvalues in various sectors of the indicator diagram is obtained. 
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     title = {Asymptotics of eigenvalues of fourth order differential operator with alternating weight function},
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S. I. Mitrokhin. Asymptotics of eigenvalues of fourth order differential operator with alternating weight function. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2018), pp. 46-58. http://geodesic.mathdoc.fr/item/VMUMM_2018_6_a6/

[1] Ilin V. A., “O skhodimosti razlozhenii po sobstvennym funktsiyam v tochkakh razryva koeffitsientov differentsialnogo operatora”, Matem. zametki, 22:5 (1977), 698–723

[2] Budaev V. D., “O bezuslovnoi bazisnosti na zamknutom intervale sistem sobstvennykh i prisoedinennykh funktsii operatora vtorogo poryadka s razryvnymi koeffitsientami”, Differents. uravneniya, 23:6 (1987), 941–952 | MR

[3] Gottlieb H. P. W., “Iso-spectral operators: some model examples with discontinuous coefficients”, J. Math. Anal. and Appl., 132 (1988), 123–137 | DOI | MR | Zbl

[4] Mitrokhin S. I., “O nekotorykh spektralnykh svoistvakh differentsialnykh operatorov vtorogo poryadka s razryvnoi vesovoi funktsiei”, Dokl. RAN, 356:1 (1997), 13–15 | MR | Zbl

[5] Gurevich A. P., Khromov A. P., “Operatory differentsirovaniya pervogo i vtorogo poryadkov so znakoperemennoi vesovoi funktsiei”, Matem. zametki, 56:1 (1994), 3–15 | MR | Zbl

[6] Mitrokhin S. I., Spektralnaya teoriya operatorov: gladkie, razryvnye, summiruemye koeffitsienty, INTUIT, M., 2009

[7] Mitrokhin S. I., “O spektralnykh svoistvakh differentsialnogo operatora s summiruemym potentsialom i gladkoi vesovoi funktsiei”, Vestn. SamGU. Estestv. seriya, 2008, no. 8(1/67), 172–187

[8] Mitrokhin S. I., “O spektralnykh svoistvakh differentsialnykh operatorov nechetnogo poryadka s summiruemym potentsialom”, Differents. uravneniya, 47:12 (2011), 1808–1811 | MR | Zbl

[9] Naimark M. A., Lineinye differentsialnye operatory, Nauka, M., 1969

[10] Levitan B. M., Sargsyan I. S., Vvedenie v spektralnuyu teoriyu, Nauka, M., 1970 | MR

[11] Bellman R., Kuk K. L., Differentsialno-raznostnye uravneniya, Mir, M., 1967

[12] Sadovnichii V. A., Lyubishkin V. A., “O nekotorykh novykh rezultatakh teorii regulyarizovannykh sledov differentsialnykh operatorov”, Differents. uravneniya, 18:1 (1982), 109–116 | MR