ArticleOriginal scientific text

Title

Asymptotic behaviour of solutions of linear differential equations with delay

Authors 1

Affiliations

  1. Department of Mathematics, Faculty of Electrical Engineering, Technical University of Brno, Areál Vut Kraví Hora 21 (XV), 602 00 Brno, Czech

Abstract

Inequalities for some positive solutions of the linear differential equation with delay ẋ(t) = -c(t)x(t-τ) are obtained. A connection with an auxiliary functional nondifferential equation is used.

Keywords

linear differential equation with delay, asymptotic behaviour

Bibliography

  1. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York 1963.
  2. J. Diblík, On existence and asymptotic behaviour of solutions of singular Cauchy problem for certain system of ordinary differential equations, Fasc. Math. 18 (1988), 51-62.
  3. J. Hale, Theory of Functional Differential Equations, Springer, New York 1977.
  4. Ph. Hartman, Ordinary Differential Equations, Wiley, New York 1964.
  5. V. B. Kolmanovskij and V. R. Nosov, Stability of Functional Differential Equations, Academic Press, 1986.
  6. V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. 2, Academic Press, 1969.
  7. K. P. Rybakowski, Ważewski's principle for retarded functional differential equations, J. Differential Equations 36 (1980), 117-138.
  8. K. P. Rybakowski, A topological principle for retarded functional differential equations of Carathéodory type, ibid. 39 (1981), 131-150.
  9. T. Ważewski, Sur un principe topologique de l'examen de l'allure asymptotique des intégrales des équations différentielles ordinaires, Ann. Soc. Polon. Math. 20 (1947), 279-313.
Pages:
131-137
Main language of publication
English
Received
1992-05-04
Accepted
1992-10-28
Published
1993
Exact and natural sciences