Skip to main content
SpringerLink
Log in

On the Solvability of Impulsive Differential-Algebraic Equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

We establish theorems on the existence and uniqueness of a solution of the impulsive differential-algebraic equation

$$\frac{d}{{dt}}[Au(t)] + Bu(t) = f(t,u(t)),$$

where the matrix A may be singular. The results are applied to the theory of electric circuits.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

REFERENCES

  1. A. M. Samoilenko, M. I. Shkil', and V. P. Yakovets', Linear Systems of Differential Equations with Degeneracies [in Ukrainian], Vyshcha Shkola, Kyiv (2000).

    Google Scholar 

  2. R. Marz, “Progress in handling differential algebraic equations,” Ann. Numer. Math., 1, 279–292 (1994).

    Google Scholar 

  3. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations, World Scientific, Singapore (1995).

    Google Scholar 

  4. F. R. Gantmakher, Theory of Matrices [in Russian], Nauka, Moscow (1966).

    Google Scholar 

  5. A. G. Rutkas, “The Cauchy problem for the equation Ax′(t) + Bx(t) = f(t),” Differents. Uravn., 11, No.11, 1996–2010 (1975).

    Google Scholar 

  6. M. V. Keldysh, “On eigenvalues and eigenfunctions of some classes of nonself-adjoint equations,” Dokl. Akad. Nauk SSSR, 77, No.1, 11–14 (1951).

    Google Scholar 

  7. M. M. Vainberg and V. A. Trenogin, Theory of Branching of Solutions of Nonlinear Equations [in Russian], Nauka, Moscow (1969).

    Google Scholar 

  8. L. Vlasenko, “Implicit linear time-dependent differential-difference equations and applications,” Math. Meth. Appl. Sci., 23, No.10, 937–948 (2000).

    Article  Google Scholar 

  9. L. A. Vlasenko and A. G. Rutkas, “On the unique solvability of one degenerate functional-differential equation,” Dopov. Nats. Akad. Nauk Ukr., No. 3, 11–16 (2003).

    Google Scholar 

  10. A. G. Rutkas and L. A. Vlasenko, “Existence, uniqueness and continuous dependence for implicit semilinear functional differential equations,” Nonlin. Anal. TMA, 55, No.12, 125–139 (2003).

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Karazin Kharkov National University, Kharkov, Ukraine

    L. A. Vlasenko

  2. Shevchenko Kiev National University, Kiev, Ukraine

    N. A. Perestyuk

Authors
  1. L. A. Vlasenko
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. N. A. Perestyuk
    View author publications

    You can also search for this author in PubMed Google Scholar

Additional information

__________

Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 57, No. 4, pp. 458–468, April, 2005.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Vlasenko, L.A., Perestyuk, N.A. On the Solvability of Impulsive Differential-Algebraic Equations. Ukr Math J 57, 551–564 (2005). https://doi.org/10.1007/s11253-005-0209-4

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s11253-005-0209-4

Keywords

Search

Navigation