Ukrainian Mathematical Journal

, Volume 53, Issue 3, pp 344–353 | Cite as

Qualitative Analysis of an Implicit Singular Cauchy Problem

  • A. E. Zernov


We consider a singular Cauchy problem for a first-order ordinary differential equation unsolved with respect to the derivative of the unknown function. We prove the existence of continuously differentiable solutions with required asymptotic properties.


Differential Equation Qualitative Analysis Ordinary Differential Equation Cauchy Problem Unknown Function 
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  1. 1.
    N. P. Erugin, A Reader for a General Course in Differential Equations [in Russian], Nauka i Tekhnika, Minsk (1972).Google Scholar
  2. 2.
    N. P. Erugin, I. Z. Shtokalo, P. S. Bondarenko, et al., A Course in Ordinary Differential Equations [in Russian], Vyshcha Shkola, Kiev (1974).Google Scholar
  3. 3.
    A. E. Zernov, “On the solvability and asymptotic properties of solutions of a singular Cauchy problem,” Differents. Uravn. 28, No. 5, 756–760 (1992).Google Scholar
  4. 4.
    I. T. Kiguradze, Some Singular Boundary-Value Problems for Ordinary Differential Equations [in Russian], Tbilisi University, Tbilisi (1975).Google Scholar
  5. 5.
    P. Hartman, Ordinary Differential Equations Wiley, New York (1964).Google Scholar
  6. 6.
    A. N. Vityuk, “A generalized Cauchy problem for a system of differential equations unsolved with respect to derivatives,” Differents. Uravn. 7, No. 9, 1575–1580 (1971).Google Scholar
  7. 7.
    V. P. Rudakov, “On the existence and uniqueness of a solution of a system of first-order differential equations partially solved with respect to derivatives,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat. No. 9, 79–84 (1971).Google Scholar
  8. 8.
    V. A. Chechik, “Investigation of systems of ordinary differential equations with singularity,” Tr. Mosk. Mat. Obshch. No. 8, 155–198 (1959).Google Scholar

Copyright information

© Plenum Publishing Corporation 2001

Authors and Affiliations

  • A. E. Zernov
    • 1
  1. 1.Odessa Polytechnic UniversityOdessa

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