Tohoku Mathematical Journal

On the existence of simple Liapunov functions for linear retarded difference-differential equations

Luis Antonio Viera Carvalho, Ettore Ferrari Infante, and John Andrew Walker

Full-text: Open access

Article information

Source
Tohoku Math. J. (2), Volume 32, Number 2 (1980), 283-297.

Dates
First available in Project Euclid: 3 May 2007

Permanent link to this document
https://projecteuclid.org/euclid.tmj/1178229644

Digital Object Identifier
doi:10.2748/tmj/1178229644

Mathematical Reviews number (MathSciNet)
MR0580283

Zentralblatt MATH identifier
0446.34070

Subjects
Primary: 34K20: Stability theory

Citation

Carvalho, Luis Antonio Viera; Infante, Ettore Ferrari; Walker, John Andrew. On the existence of simple Liapunov functions for linear retarded difference-differential equations. Tohoku Math. J. (2) 32 (1980), no. 2, 283--297. doi:10.2748/tmj/1178229644. https://projecteuclid.org/euclid.tmj/1178229644


Export citation

References

  • [1] W. DEB. CASTELAN AND E. F. INFANTE, A Liapunov functional for a matrix difference differential equation, J. Diff. Equations 29 (1978), 439-451.
  • [2] R. D. DRIVER, Linear differential systems with small delays, J. Diff. Equations 21 (1976), 148-166.
  • [3] J. K. HALE, Functional Differential Equations, Appl. Math. Sciences, Vol. 3, Springer Verlag, Berlin-Heidelberg-New York, 1975.
  • [4] J. K. HALE, Theory of Functional Differential Equations, Applied Math. Sciences, Vol 3, Springer-Verlag, Berlin-Heidelberg-New York, 1977.
  • [5] J. K. HALE, Dynamical Systems and Stability, J. Math. Anal, and Appl. 26 (1969), 39-59
  • [6] J. K. HALE, E. F. INFANTE AND F. P. TSEN, Stability in delay equations for all delays, Center for Dynamical Systems Report, Brown University, 1979.
  • [7] E. F. INFANTE AND J. A. WALKER, A Liapunov functional for a scalar differentia difference equation, Proc. Royal Soc. of Edinburgh 79A (1977), 307-316.
  • [8] M. KRASOVSKII, Stability of Motion, Stanford Univ. Press, 1963
  • [9] B. S. RAZUMIKHIN, Application of Liapunov's Method to problems in the stability o systems with delays, Autom. i Telemech. 21 (1960), 740-749.
  • [10] K. YOSIDA, Functional Analysis, 4th Edition, Springer-Verlag, Berlin-Heidelberg-Ne York, 1974.
  • [11] T. YOSHIZAWA, Stability Theory by Liapunov's Second Method, Math. Soc. Japan, 1966
  • [12] T. YOSHIZAWA, Stability Theory and the Existence of Periodic Solutions and Almos Periodic Solutions, Appl. Math. Sciences Vol. 14, Springer-Verlag, Berlin-Heidelberg-New York, 1975.