Abstract
For systems ofq linear differential equations ofnth order with polynomial matrix coefficients, a fundamental family of formal solutions defined in a certain sector of a complex plane is constructed by using the Laplace contour integral. For large positive values of an independent variable, the asymptotic representations of indicated solutions are obtained.
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References
N. N. Ivanyuk,On Investigation of Solutions of a Linear System of nth-Order Differential Equations Near Singular Points [in Russian], Candidate Degree Thesis (Physics and Mathematics), Khmel'nitskii (1989).
N. I. Gavrilov,Methods of the Theory of Ordinary Differential Equations [in Russian], Vysshaya Shkola, Moscow (1962).
W. Wasov,Asymptotic Expansions for Ordinary Differential Equations, Wiley-Interscience, New York (1965).
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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 1, pp. 30–38, January, 1995.
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Ivanyuk, M.M. Integration of a class of systems of differential equations by using a contour integral. Ukr Math J 47, 32–41 (1995). https://doi.org/10.1007/BF01058793
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DOI: https://doi.org/10.1007/BF01058793