Quarterly of Applied Mathematics

Quarterly of Applied Mathematics

Online ISSN 1552-4485; Print ISSN 0033-569X

   
 
 

 

A procedure for determination of the exponential stability of certain differential-difference equations


Author: R. Datko
Journal: Quart. Appl. Math. 36 (1978), 279-292
MSC: Primary 34K20
DOI: https://doi.org/10.1090/qam/508772
MathSciNet review: 508772
Full-text PDF Free Access

Abstract | References | Similar Articles | Additional Information

Abstract: Certain continuity properties of the spectra of linear autonomous differential-difference equations which depend on a parameter are developed. These results are used to obtain a practical criterion for determination of the exponential stability of these systems.


References [Enhancements On Off] (What's this?)

  • [1] A. S. Besicovitch, Almost periodic functions, Dover Publications. Inc., 1954 MR 0068029
  • [2] H. Bohr, Collected Mathematical Works, Vol. 1, Dansk Matemetisk Forening, KØbenhavn, 1952. See also H. Bohr, Über die gleich Mässige Konvergenz Dirichletsher Reihen, J. Reine Angew. Math. 143, 203-211 (1913) MR 0057790
  • [3] R. Datko, Representation and stability of linear differential-difference equations in a Banach space, to appear. MR 0486927
  • [4] R. Datko, The stabilization of linear functional differential equations, in Calculus of variations and control theory, ed. D. L. Russell, Academic Press, Inc., New York, 1975, pp. 353-369 MR 0421794
  • [5] L. E. El'sgol'ts and S. B. Norkin, Introduction to the theory and application of differential equations with deviating arguments, Academic Press, New York, 1973 MR 0352647
  • [6] J. Hale, Theory of functional differential equations, Springer-Verlag, New York, 1977 MR 0508721
  • [7] D. Henry, Linear autonomous neutral functional differential equations, J. Diff. Eqs. 15, 106-128 (1974) MR 0338520
  • [8] S. Saks and A. Zygmund, Analytic functions, Elsevier Publishing Co., New York, 1971

Similar Articles

Retrieve articles in Quarterly of Applied Mathematics with MSC: 34K20

Retrieve articles in all journals with MSC: 34K20


Additional Information

DOI: https://doi.org/10.1090/qam/508772
Article copyright: © Copyright 1978 American Mathematical Society

American Mathematical Society