Skip to main content
Log in

Uniqueness of solutions of impulsive hyperbolic differential-functional equations

  • Published:
Ukrainian Mathematical Journal Aims and scope

Abstract

For impulsive partial differential-functional equations, we prove the theorems on existence and uniqueness of solutions and their continuous dependence on the right-hand sides of the equations.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References

  1. V. Lakshmikantham and S. Leela,Differential and Integral Inequalities, New York-London (1969).

  2. J. Szarski,Differential Inequalities, Warszawa(1967).

  3. Z. Kamont, “On the Cauchy problem for a system of first order partial differential-functional equations,”Serdica Bulg. Math. Publ.,5, 327–339 (1979).

    MATH  MathSciNet  Google Scholar 

  4. Z. Kamont, “On the Chaplygin method for partial differential-functional equations of the first order,”Ann. Polon. Math.,38, No. 1, 27–46 (1980).

    MATH  MathSciNet  Google Scholar 

  5. P. Brandi, Z. Kamont, and A. Salvadori, “Differential and differential-difference inequalities related to mixed problems for first order partial differential-functional equations,”Atti Semin. e Mat. Fis. Univ. Modena,39, 255–276 (1991).

    MATH  MathSciNet  Google Scholar 

  6. D. Jaruszewska-Walczak, “Differential-functional inequalities related to initial-boundary problems for first order partial differential-functional equations,”Periodica Math. Hung.,26, No. 2, 163–174 (1993).

    Article  MATH  MathSciNet  Google Scholar 

  7. D. Bainov, V. Lakshmikantham, and P. Simeonov,Theory of Impulsive Differential Equations, World Scientific, Singapore (1989).

    MATH  Google Scholar 

  8. A. M. Samoilenko and N. A. Perestyuk,Impulsive Differential Equations [in Russian], Kiev (1987), World Scientific, Ser. Nonlinear Sci., Ser. A.,14 (1995).

  9. S. Rogovchenko,Periodic Solutions of Hyperbolic Systems with Fixed Moments of Impulse Effect [in Russian], Preprint No. 88.8, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1988).

    Google Scholar 

  10. Yu. V. Rogovchenko and S. I. Trofimchuk,Periodical Solutions of Weakly Nonlinear Impulsive Partial Differential Equations of the Parabolic Type and Their Stability [in Russian], Preprint No. 86–65, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986).

    Google Scholar 

  11. Yu. V. Rogovchenko and S. I. Trofimchuk, “Restricted and periodical solutions of weakly non-linear impulse evolutionary systems,”Ukr. Mat. Zh.,39, No. 2. -P. 260–264 (1987).

    MATH  MathSciNet  Google Scholar 

  12. L. H. Erbe, H. I. Freedman, X. Z. Liu, J. H. Wu, “Comparison principles for impulsive parabolic equations with applications to models of single species growth,”J. Austral. Math. Soc. Ser. B,32, 382–400 (1991).

    Article  MATH  MathSciNet  Google Scholar 

  13. D. Bainov, Z. Kamont, and E. Minchev, “On first order impulsive partial differential inequalities,”Appl. Math. Comp.,61, 207–230 (1994).

    Article  MATH  MathSciNet  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

Published in Ukrainskii Matematicheskii Zhurnal, Vol. 51, No. 2, pp. 241–250, February, 1999.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Jaruszewska-Walczak, D. Uniqueness of solutions of impulsive hyperbolic differential-functional equations. Ukr Math J 51, 269–280 (1999). https://doi.org/10.1007/BF02513479

Download citation

  • Received:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF02513479

Keywords

Navigation