Construction of asymptotics of solutions to the Sturm–Liouville differential equations in the class of oscillating coefficients
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2023), pp. 61-65 Cet article a éte moissonné depuis la source Math-Net.Ru

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The article is focused on the development of a method allowing one to construct asymptotics for solutions to ODEs of arbitrary order with oscillating coefficients on the semiaxis. The idea of the method is presented on the example of studying the asymptotics of the Sturm–Liouville equation.
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     title = {Construction of asymptotics of solutions to the {Sturm{\textendash}Liouville} differential equations in the class of oscillating coefficients},
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N. F. Valeev; È. A. Nazirova; Ya. T. Sultanaev. Construction of asymptotics of solutions to the Sturm–Liouville differential equations in the class of oscillating coefficients. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 5 (2023), pp. 61-65. http://geodesic.mathdoc.fr/item/VMUMM_2023_5_a8/

[1] Zettl A., Sturm–Liouville Theory, Math. Surv. and Mon., 121, Amer. Math. Soc., Providence, RI, 2005 | MR | Zbl

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

[3] Sultanaev Ya.T., “Asimptotika reshenii obyknovennykh differentsialnykh uravnenii v vyrozhdennom sluchae”, Tr. seminara im. I. G. Petrovskogo, 13, 1988, 36–55 | MR

[4] Everitt W.N., Marcus L., “Boundary value problem and symplectic algebra for ordinary differential and quazi-differential operators”, Math. Surv. and Mon. Amer. Math. Soc, 60 (1999), 1–60 | MR

[5] Mirzoev K.A., Konechnaya N.N., Shkalikov A.A., “Ob asimptotike reshenii differentsialnykh uravnenii s singulyarnymi koeffitsientami”, Matem. zametki, 120:2 (2019), 240–251

[6] Konechnaya N.N., Mirzoev K.A., Sultanaev Ya.T., “On the asymptotics of solutions of some classes of linear differential equations”, Azerbaijan J. Math, 10:1 (2020), 162–171 | MR | Zbl

[7] Nesterov P.N., “Postroenie asimptotiki reshenii odnomernogo uravneniya Shredingera s bystro ostsilliruyuschim potentsialom”, Matem. zametki, 80:2 (2006), 240–250 | DOI | Zbl

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

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

[10] Valeev N.F., Myakinova O.V, Sultanaev Ya.T., “Ob asimptotike reshenii singulyarnogo differentsialnogo uravneniya $n$-go poryadka s neregulyarnymi koeffitsientami”, Matem. zametki, 104:4 (2018), 626–631 | DOI | MR | Zbl

[11] Valeeva L.N., Nazirova E.A., Sultanaev Ya.T., “Ob odnom metode issledovaniya asimptotiki reshenii differentsialnykh uravnenii Shturma–Liuvillya s bystro ostsilliruyuschimi koeffitsientami”, Matem. zametki, 112:6 (2022), 935–940 | DOI | MR | Zbl