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Ukrainian Mathematical Journal

, Volume 45, Issue 10, pp 1644–1648 | Cite as

Existence and asymptotic properties of solutions of a real system of differential equations unresolved with respect to the derivative

  • L. G. Prosenyuk
Brief Communications

Abstract

A system of differential equations unresolved with respect to a derivative is studied. Sufficient conditions for the existence of solutions with singular initial data are found. The dimensionality of the set of these solutions is determined and their asymptotic properties are studied.

Keywords

Differential Equation Initial Data Real System Asymptotic Property Singular Initial Data 
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

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    G. I. Zaporozhets, “Investigation of a homogeneous first-order differential equation unresolved with respect to the derivative,”Differents. Uravn.,1, No. 5, 567–581 (1961).Google Scholar
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    V. P. Rudakov, “On the existence and uniqueness of solutions of the systems of first-order differential equations partially resolved with respect to the derivatives,”Izv. Vyssh. Uchebn. Zaved., Ser. Mat., No. 9, 79–85 (1971).Google Scholar
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    B. Ricceri, “Solutions lipschitziennez differentielles sous forme implicite,”C. R. Acad. Sci., Ser. 1,295, No. 3, 245–248 (1982).Google Scholar
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    P. Hartman,Ordinary Differential Equations [Russian translation], Mir, Moscow (1970).Google Scholar
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    K. Borsuk,Theory of Retracts [Russian translation], Mir, Moscow (1971).Google Scholar

Copyright information

© Plenum Publishing Corporation 1994

Authors and Affiliations

  • L. G. Prosenyuk
    • 1
  1. 1.Odessa Institute of Civil EngineersOdessa

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