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ON THE ASYMPTOTICS OF SOLUTIONS OF ORDINARY DIFFERENTIAL EQUATIONS OF ODD ORDER
- Authors: Sultanaev Y.T1,2, Mardanov B.I2, Nazirova E.A3
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Affiliations:
- Moscow Center for Fundamental and Applied Mathematics
- Akmulla Bashkir State Pedagogical University
- Ufa University of Science and Technology
- Issue: Vol 61, No 2 (2025)
- Pages: 221-228
- Section: ORDINARY DIFFERENTIAL EQUATIONS
- URL: https://journal-vniispk.ru/0374-0641/article/view/299127
- DOI: https://doi.org/10.31857/S0374064125020079
- EDN: https://elibrary.ru/HWORFY
- ID: 299127
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Abstract
The asymptotic behavior for large values of the independent variable of the fundamental system of solutions of linear differential equations generated by a symmetric two-term differential expression of arbitrary odd order is investigated, depending on the coefficients of the highest derivative and the free term.
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About the authors
Ya. T Sultanaev
Moscow Center for Fundamental and Applied Mathematics; Akmulla Bashkir State Pedagogical University
Email: sultanaevyt@gmail.com
B. I Mardanov
Akmulla Bashkir State Pedagogical University
Email: mardanov_bulat@list.ru
E. A Nazirova
Ufa University of Science and Technology
Email: ellkid@gmail.com
References
- Valeeva, L.N., Nazirova, E.A., and Sultanaev, Ya.T., On a method for studying the asymptotics of solutions of Sturm–Liouville differential equations with rapidly oscillating coefficients, Math. Notes, 2022, vol. 112, no. 6, pp. 1059–1064.
- Valeev, N.F., Nazirova, E.A., and Sultanaev, Ya.T., On a new approach for studying asymptotic behavior of solutions to singular differential equations, Ufa Math. J., 2015, vol. 7, no. 3, pp. 9–14.
- Valeev, N.F., Myakinova, O.V., and Sultanaev, Ya.T., On the asymptotics of solutions of a singular 𝑛th-order differential equation with nonregular coefficients, Math. Notes, 2018, vol. 104, no. 4, pp. 606–611.
- Rossmann, W. Lie Groups — an Introduction Through Linear Groups / W. Rossmann. — Oxford : Oxford University Press, 2006. — 265 p.
- Everitt, W.N. Boundary value problem and symplectic algebra for ordinary differential and quasidifferential operators / W.N. Everitt, L. Marcus. — Providence : Amer. Math. Soc., 1999. — 187 p.
- Naimark, M.A., Lineynyye differentsial’nyye operatory (Linear Differential Operators), Moscow: Nauka, 1969.
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