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JOURNALS // Sibirskie Èlektronnye Matematicheskie Izvestiya [Siberian Electronic Mathematical Reports] // Archive

Sib. Èlektron. Mat. Izv., 2023 Volume 20, Issue 1, Pages 251–261 (Mi semr1584)

Differentical equations, dynamical systems and optimal control

On uniform asymptotics of solutions of second-order differential equations with meromorphic coefficients in a neighborhood of singular points

M. V. Korovinaa, H. A. Matevossianbc

a Lomonosov Moscow State University, Russia, 119992, Moscow, Leninskie Gory, 1
b Federal Research Center "`Computer Science and Control"', Russian Academy of Sciences, Russia, 119333, Moscow, Vavilov str., 40-42, R374
c Moscow Aviation Institute (National Research University), Russia, 125993, Moscow, Volokolamskoe Shosse, 4

Abstract: We consider the problem of obtaining asymptotics for solutions of differential operators in a neighborhood of an irregular singular point; more precisely, the construction of uniform asymptotics for solutions of linear differential equations with second-order meromorphic coefficients in a neighborhood of a singular point. Examples are also given that confirm the relevance of the results obtained in the theory of equations of mathematical physics.

Keywords: Second-order differential operator, meromorphic coefficients, singular points.

UDC: 517.95

MSC: 35B40, 34M05, 35J05

Received April 15, 2022, published March 9, 2023

DOI: 10.33048/semi.2023.20.020



© Steklov Math. Inst. of RAS, 2025