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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. Korovina
Lomonosov Moscow State University, Faculty of the VMC
Russian Federation

Maria V. Korovina

1, p. 52, Leninskie gory, Moscow 119192



References

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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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ISSN 2411-9326 (Print)
ISSN 2587-876X (Online)