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.
@article{bwmeta1.element.bwnjournal-article-apmv58z2p131bwm,
author = {Josef Dibl\'\i k},
title = {Asymptotic behaviour of solutions of linear differential equations with delay},
journal = {Annales Polonici Mathematici},
volume = {58},
year = {1993},
pages = {131-137},
zbl = {0784.34053},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-apmv58z2p131bwm}
}
Josef Diblík. Asymptotic behaviour of solutions of linear differential equations with delay. Annales Polonici Mathematici, Tome 58 (1993) pp. 131-137. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-apmv58z2p131bwm/
[000] [1] R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York 1963. | Zbl 0105.06402
[001] [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. | Zbl 0664.34007
[002] [3] J. Hale, Theory of Functional Differential Equations, Springer, New York 1977. | Zbl 0352.34001
[003] [4] Ph. Hartman, Ordinary Differential Equations, Wiley, New York 1964.
[004] [5] V. B. Kolmanovskij and V. R. Nosov, Stability of Functional Differential Equations, Academic Press, 1986. | Zbl 0593.34070
[005] [6] V. Lakshmikantham and S. Leela, Differential and Integral Inequalities, Vol. 2, Academic Press, 1969. | Zbl 0177.12403
[006] [7] K. P. Rybakowski, Ważewski's principle for retarded functional differential equations, J. Differential Equations 36 (1980), 117-138. | Zbl 0407.34056
[007] [8] K. P. Rybakowski, A topological principle for retarded functional differential equations of Carathéodory type, ibid. 39 (1981), 131-150. | Zbl 0477.34048
[008] [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. | Zbl 0032.35001