Asymptotic behaviour of solutions of linear differential equations with delay

Josef Diblík

Annales Polonici Mathematici (1993)

  • Volume: 58, Issue: 2, page 131-137
  • ISSN: 0066-2216

Abstract

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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.

How to cite

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Josef Diblík. "Asymptotic behaviour of solutions of linear differential equations with delay." Annales Polonici Mathematici 58.2 (1993): 131-137. <http://eudml.org/doc/262494>.

@article{JosefDiblík1993,
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.},
author = {Josef Diblík},
journal = {Annales Polonici Mathematici},
keywords = {linear differential equation with delay; asymptotic behaviour; inequalities; positive solutions; delay functional differential equation; growth},
language = {eng},
number = {2},
pages = {131-137},
title = {Asymptotic behaviour of solutions of linear differential equations with delay},
url = {http://eudml.org/doc/262494},
volume = {58},
year = {1993},
}

TY - JOUR
AU - Josef Diblík
TI - Asymptotic behaviour of solutions of linear differential equations with delay
JO - Annales Polonici Mathematici
PY - 1993
VL - 58
IS - 2
SP - 131
EP - 137
AB - 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.
LA - eng
KW - linear differential equation with delay; asymptotic behaviour; inequalities; positive solutions; delay functional differential equation; growth
UR - http://eudml.org/doc/262494
ER -

References

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  1. [1] R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York 1963. Zbl0105.06402
  2. [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. Zbl0664.34007
  3. [3] J. Hale, Theory of Functional Differential Equations, Springer, New York 1977. Zbl0352.34001
  4. [4] Ph. Hartman, Ordinary Differential Equations, Wiley, New York 1964. 
  5. [5] V. B. Kolmanovskij and V. R. Nosov, Stability of Functional Differential Equations, Academic Press, 1986. Zbl0593.34070
  6. [6] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. 2, Academic Press, 1969. Zbl0177.12403
  7. [7] K. P. Rybakowski, Ważewski's principle for retarded functional differential equations, J. Differential Equations 36 (1980), 117-138. Zbl0407.34056
  8. [8] K. P. Rybakowski, A topological principle for retarded functional differential equations of Carathéodory type, ibid. 39 (1981), 131-150. Zbl0477.34048
  9. [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. Zbl0032.35001

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