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The asymptotic behavior of solutions of ordinary differential equations in the degenerate case

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Abstract

We investigate the asymptotic behavior of the fundamental system of solutions of a homogeneous linear differential equation of high order on the semiaxis for large values of the argument in the case when the contributions of the coefficients to the asymptotic formulae are the same and one of them increases indefinitely together with the argument. We find the deficiency indices of the corresponding minimal operator.

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Authors
  1. Ya. T. Sultanaev
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Additional information

Translated from Trudy Seminara imeni I. G. Petrovskogo, No. 13, pp. 36–55, 1988.

In conclusion the author expresses his deep gratitude to A. G. Kostyuchenko for a discussion of the results.

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Sultanaev, Y.T. The asymptotic behavior of solutions of ordinary differential equations in the degenerate case. J Math Sci 50, 1364–1380 (1990). https://doi.org/10.1007/BF01097029

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  • DOI: https://doi.org/10.1007/BF01097029

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