Uniform Asymptotics of Solutions of Second-Order Differential Equations with Meromorphic Coefficients in a Neighborhood of Singular Points and Their Applications

Maria V. Korovina and Hovik A. Matevossian
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Maria V. Korovina: Faculty of Computational Mathematics and Cybernetics, Lomonosov Moscow State University, Moscow 119991, Russia
Hovik A. Matevossian: Federal Research Center “Computer Science and Control”, Russian Academy of Sciences, Moscow 119333, Russia

Mathematics, 2022, vol. 10, issue 14, 1-21

Abstract: In this paper, we consider the problem of obtaining the asymptotics of solutions of differential operators in a neighborhood of an irregular singular point. More precisely, we construct uniform asymptotics for solutions of linear differential equations with second-order meromorphic coefficients in a neighborhood of a singular point and apply the results obtained to the equations of mathematical physics. The main results related to the construction of uniform asymptotics are obtained using resurgent analysis methods applied to differential equations with irregular singularities. These results allow us to construct asymptotics for any second-order equations with meromorphic coefficients—that is, with an arbitrary order of degeneracy. This also allows one to determine the type of a singular point and highlight the cases where the point is non-singular or regular.

Keywords: second-order differential operator; meromorphic coefficients; singular points (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2022
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