Geodesic
Spectral properties of differential operators with oscillating coefficients
Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 2, pp. 179-195 
N. F. Valeev; Ya. T. Sultanaev; É. A. Nazirova. Spectral properties of differential operators with oscillating coefficients. Trudy Moskovskogo matematičeskogo obŝestva, Trudy Moskovskogo Matematicheskogo Obshchestva, Tome 80 (2019) no. 2, pp. 179-195. http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a3/
@article{MMO_2019_80_2_a3,
     author = {N. F. Valeev and Ya. T. Sultanaev and \'E. A. Nazirova},
     title = {Spectral properties of differential operators with oscillating coefficients},
     journal = {Trudy Moskovskogo matemati\v{c}eskogo ob\^{s}estva},
     pages = {179--195},
     year = {2019},
     volume = {80},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a3/}
}
TY  - JOUR
AU  - N. F. Valeev
AU  - Ya. T. Sultanaev
AU  - É. A. Nazirova
TI  - Spectral properties of differential operators with oscillating coefficients
JO  - Trudy Moskovskogo matematičeskogo obŝestva
PY  - 2019
SP  - 179
EP  - 195
VL  - 80
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a3/
LA  - ru
ID  - MMO_2019_80_2_a3
ER  - 
%0 Journal Article
%A N. F. Valeev
%A Ya. T. Sultanaev
%A É. A. Nazirova
%T Spectral properties of differential operators with oscillating coefficients
%J Trudy Moskovskogo matematičeskogo obŝestva
%D 2019
%P 179-195
%V 80
%N 2
%U http://geodesic.mathdoc.fr/item/MMO_2019_80_2_a3/
%G ru
%F MMO_2019_80_2_a3

Voir la notice du chapitre de livre provenant de la source Math-Net.Ru

We study the properties of singular Sturm-Liouville operators in Hilbert spaces. Although the literature on the topic is immense, there are a number of questions that have yet to be solved, for example, those pertaining to the behavior of solutions of the Sturm-Liouville equation with an irregular potential at infinity. This problem is topical not only for being of interest in itself but also because it naturally arises when dealing with questions related to the spectral properties of the Sturm-Liouville operator.

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

[2] Fedoryuk M. F., Asimptoticheskie metody dlya lineinykh obyknovennykh differentsialnykh uravnenii, Nauka, M., 1983

[3] Eastham M. S. P., Grudniewicz C. G. M., “Asymptotic theory and deficiency indices for higher-order selfadjoint differential equations”, J. London Math. Soc. (2), 24:2 (1981), 255–271 | DOI | MR | Zbl

[4] Everitt W. N., Zettl A., “Generalized symmetric ordinary differential expressions. I. The general theory”, Nieuw Arch. Wisk. (3), 27:3 (1979), 363–397 | MR | Zbl

[5] Eastham M. S. P., “Limit-circle differential expressions of the second order with an oscillating coefficient”, Quart. J. Math. Ser. 2, 24:94 (1973), 257–263 | DOI | MR | Zbl

[6] Naboko S. N., Pushnitskii A. B., “Tochechnyi spektr, lezhaschii na nepreryvnom, dlya slabo vozmuschennykh operatorov tipa Shtarka”, Funkts. analiz i ego pril., 29:4 (1995), 31–44 | Zbl

[7] Murtazin Kh. Kh., Sultanaev Ya. T., “K formulam raspredeleniya sobstvennykh chisel nepoluogranichennogo operatora Shturma–Liuvillya”, Matem. zametki, 28:4 (1980), 545–553 | Zbl

[8] Makina N. K., Nazirova E. A., Sultanaev Ya. T., “O metodakh issledovaniya asimptoticheskogo povedeniya reshenii singulyarnykh differentsialnykh uravnenii”, Matem. zametki, 96:4 (2014), 627–632 | DOI | Zbl

[9] Valeev N. F., Nazirova E. A., Sultanaev Ya. T., “O novom podkhode k izucheniyu asimptoticheskogo povedeniya reshenii singulyarnykh differentsialnykh uravnenii”, Ufimsk. matem. zhurn., 7:3 (2015), 9–15

[10] Valeev N. F., Sultanaev Ya. T., “Ob indeksakh defekta operatora Shturma–Liuvillya s bystroostsilliruyuschim vozmuscheniem”, Doklady RAN, 374:6 (2000), 732–734 | Zbl