A method for constructing asymptotics to solutions of differential equations with holomorphic coefficients in the neightborhood of irregular singular points
https://doi.org/10.25587/2411-9326-2025-1-119-121
Abstract
The work is devoted to the Poincare problem in the analytical theory of differential equations. Namely the constructions of asymptotic of solutions of ordinary differential equations with holomorphic or meromorphic coefficients in the vicinity of irregular points.The paper provides the general view of the asymptotic of solutions of differential equations with meromorphic coefficients in the neighborhood of irregular points.
About the Author
M. V. KorovinaRussian Federation
Maria V. Korovina
1, p. 52, Leninskie gory, Moscow 119192
References
1. Poincar´e H. Sur les int´egrales irr´eguli`eres des ´equations lin´eaires // Acta Math. 1886. V. 8. P. 295–344.
2. Poincar´e H. Analysis of the mathematical and natural works of Henri Poincar´e. Selected Works in Three Volumes. Moscow: Nauka, 1974. V. 3.
3. Kats D. S. Computation of the asymptotics of solutions for equations with polynomial degeneration of the coefficients // Differ. Equ. 2015. V. 51. P. 1589–1594.
4. Korovina M. V., Shatalov V. E. Differential equations with degeneration and resurgent analysis // Differ. Equ. 2010. V. 46, N 9. P. 1267–1286.
5. Korovina M. V. Asymptotics of solutions of equations with higher degenerations // Differ. Equ. 2012. V. 48, N 5. P. 717-729.
6. Korovina M. V. Asymptotics of solutions of linear differential equations with holomorphic coefficients in the neighborhood of an infinitely distant point // Mathematics. 2020. V. 8. 2249.
7. Korovina M. V. Uniform asymptotics of solutions to linear differential equations with holomorphic coefficients in the neighborhood of an infinitely // Lobachevskii J. Math. 2023. V. 44, N 7. P. 2765–2780.
8. Sternin B. Yu., Shatalov V. E. Borel–Laplace transform and asymptotic theory. Introduction to resurgent analysis. FL USA: Boca Raton, 1996.
Review
For citations:
Korovina M.V. A method for constructing asymptotics to solutions of differential equations with holomorphic coefficients in the neightborhood of irregular singular points. Mathematical notes of NEFU. 2025;32(1):119-121. (In Russ.) https://doi.org/10.25587/2411-9326-2025-1-119-121
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