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Ukrainian Mathematical Journal

, Volume 55, Issue 12, pp 2060–2063 | Cite as

Qualitative Investigation of the Singular Cauchy Problem F(t, x, x′) = 0, x(0) = 0

  • A. E. Zernov
  • Yu. V. Kuzina
Article

Abstract

We prove the existence and uniqueness of a continuously differentiable solution with required asymptotic properties.

Keywords

Cauchy Problem Asymptotic Property Qualitative Investigation Differentiable Solution Singular Cauchy Problem 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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REFERENCES

  1. 1.
    N. P. Erugin, General Course of Differential Equations. A Textbook [in Russian], Nauka i Tekhnika, Minsk (1972).Google Scholar
  2. 2.
    I. T. Kiguradze, “On the Cauchy problem for singular systems of ordinary differential equations,” Differents. Uravn., 1, No. 10, 1271-1291 (1965).Google Scholar
  3. 3.
    V. A. Chechik, “Investigation of systems of ordinary differential equations with singularity,” Tr. Mosk. Mat. Obshch., No. 8, 155-198 (1959).Google Scholar
  4. 4.
    A. N. Vityuk, “Generalized Cauchy problem for a system of differential equations unsolved with respect to derivatives,” Differents. Uravn., 7, No. 9, 1575-1580 (1971).Google Scholar
  5. 5.
    V. P. Rudakov, “On the existence and uniqueness of solutions of systems of first-order differential equations partially resolved with respect to derivatives,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 9, 79-84 (1971).Google Scholar
  6. 6.
    R. Conti, “Sulla risoluzione dell'equazione F(t, x, dx/ dt) =0,” Ann. Mat. Pura Appl., No. 48, 97-102 (1959).Google Scholar
  7. 7.
    Z. Kowalski, “A difference method of solving the differential equation y'=h(t, y, y, y')Ann. Pol. Math.,16, No. 2, 121-148 (1965). Google Scholar
  8. 8.
    B. P. Demidovich, Lectures on the Mathematical Theory of Stability [in Russian], Nauka, Moscow (1967).Google Scholar
  9. 9.
    V. V. Nemytskii and V. V. Stepanov, Qualitative Theory of Differential Equations [in Russian], Gostekhteorizdat, Moscow (1949).Google Scholar
  10. 10.
    A. E. Zernov, “Qualitative analysis of an implicit singular Cauchy problem,” Ukr. Mat. Zh., 53, No. 3, 302-310 (2001).Google Scholar

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • A. E. Zernov
    • 1
  • Yu. V. Kuzina
    • 1
  1. 1.South-Ukrainian Pedagogic UniversityOdessa

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