Asymptotic behavior of solutions of a differential equation partially solved with respect to the derivative.

*(English. Russian original)*Zbl 0521.34003
Sib. Math. J. 23, 654-662 (1983); translation from Sib. Mat. Zh. 23, No. 5, 80-91 (1982).

##### MSC:

34A99 | General theory for ordinary differential equations |

34E05 | Asymptotic expansions of solutions to ordinary differential equations |

##### Keywords:

formal series solution##### References:

[1] | A. V. Pkhakadze and A. A. Shestakov, ?Classification of singular points of a first-order differential equation not solved with respect to the derivative,? Mat. Sb.,49, No. 1, 3-12 (1959). · Zbl 0086.28401 |

[2] | M. A. Dautov and L. M. Muratov, ?Asymptotic representation of solutions of a first-order polynomial differential equation,? Izv. Vyssh. Uchebn. Zaved., Mat.,4, 61-68 (1964). |

[3] | A. E. Zernov, ?Solutions of a system of singular differential equations partially solved with respect to the derivatives,? Mat. Zametki,24, No. 3, 349-357 (1978). |

[4] | A. V. Kostin, ?Asymptotic properties of solutions of ordinary first-order differential equations,? Differents. Uravn.,4, No. 7, 1184-1195 (1968). |

[5] | R. G. Grabovskaya and I. Diblik, ?Asymptotic behavior of solutions of systems of differential equations not solved with respect to the derivatives,? Dep. VINITI, No. 1786-78 Dep. |

[6] | I. Diblik, ?Asymptotic behavior of solutions of Emden-Fowler type equations not solved with respect to the highest derivative,? in: Fifth All-Union Conference on Qualitative Theory of Differential Equations, Abstracts of Reports, Kishinev (1979), pp. 60-61. |

[7] | R. G. Grabovskaya and I. Diblik, ?Asymptotic behavior of solutions of an equation not solved with respect to the derivative,? Differents. Integr. Uravn., No. 3, 191-192, Gor’kii (1979). |

[8] | F. Hartmann, Ordinary Differential Equations [Russian translation], Mir, Moscow (1970). |

[9] | G. M. Fikhtengol’ts, Course of Differential and Integral Calculus [in Russian], Nauka, Moscow (1966). |

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