Jump to ContentJump to Main Navigation
Show Summary Details
More options …

Demonstratio Mathematica

Editor-in-Chief: Vetro, Calogero


Covered by:
Web of Science - Emerging Sources Citation Index
Scopus
MathSciNet


CiteScore 2017: 0.28
SCImago Journal Rank (SJR) 2017: 0.231
Source Normalized Impact per Paper (SNIP) 2017: 0.443
Mathematical Citation Quotient (MCQ) 2017: 0.12
ICV 2017: 121.78



Open Access
Online
ISSN
2391-4661
See all formats and pricing
More options …
Volume 47, Issue 4

Issues

The Existence of a Unique Solution of the Hyperbolic Functional Differential Equation

Adrian Karpowicz
Published Online: 2014-12-11 | DOI: https://doi.org/10.2478/dema-2014-0070

Abstract

We consider the Z. Szmydt problem for the hyperbolic functional differential equation. We prove a theorem on existence of a unique classical solution and the Carathéodory solution of the hyperbolic equation.

Keywords: and phrases existence theorem; functional differential equation; hyperbolic equations

References

  • [1] E. Berkson, T. A. Gillespie, Absolutely continuous functions of two variables and well-bounded operators, J. London Math. Soc. 30 (1984), 305-321.Google Scholar

  • [2] T. Człapinski, Hyperbolic functional differential equations, Gdansk, 1999.Google Scholar

  • [3] K. Deimling, A Carathéodory theory for systems of integral equations, Ann. Mat. Pura Appl. 86 (1970), 217-260.Google Scholar

  • [4] A. Karpowicz, The existence of Carathéodory solutions of hyperbolic functional differential equations, Discuss. Math. Differ. Incl. Control Optim. 30 (2010), 121-140.Google Scholar

  • [5] M. Krzyzanski, Partial Differential Equations of Second Order, Vol. 1, Warszawa, PWN, 1971.Google Scholar

  • [6] M. Krzyzanski, Partial Differential Equations of Second Order, Vol. 2, Warszawa, PWN, 1971.Google Scholar

  • [7] A. Lasota, Sur l’existence et l’unicité des solutions d’un probleme de Mlle Z. Szmydt relatif á l’équation de la corde vibrante en fonction de la position du point initial, Ann. Polon. Math. 9 (1960), 49-53.Google Scholar

  • [8] Z. Szmydt, Sur l’existence de solutions de certains nouveaux problemes pour un systeme d’équations différentielles hyperboliques du second ordre a deux variables indépendantes, Ann. Polon. Math. 4 (1957), 40-60.Google Scholar

  • [9] Z. Szmydt, Sur l’existence d’une solution unique de certains problemes pour un systeme d’équations différentielles hyperboliques du second ordre a deux variables indépendantes, Ann. Polon. Math. 4 (1957), 165-182. Google Scholar

About the article

Received: 2013-04-29

Revised: 2014-04-29

Published Online: 2014-12-11

Published in Print: 2014-12-01


Citation Information: Demonstratio Mathematica, Volume 47, Issue 4, Pages 866–877, ISSN (Online) 2391-4661, ISSN (Print) 0420-1213, DOI: https://doi.org/10.2478/dema-2014-0070.

Export Citation

© by Adrian Karpowicz. This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License. BY-NC-ND 3.0

Comments (0)

Please log in or register to comment.
Log in