Abstract
We establish new properties of solutions of the functional differential equation {fx153-01} in the neighborhood of the singular point t = +∞.
Similar content being viewed by others
References
T. Kato and J. B. McLeod, “The functional-differential equation y′(x) = ay(λx) + by(x),” Bull. Amer. Math. Soc. 77. 891–937 (1971).
N. G. de Bruijn, “The difference-differential equation {ie157-01}. I, II,” Ned. Akad. Wetensch. Proc., Ser. A, Math., 15, 449–464 (1953).
P. O. Frederickson, “Series solutions for certain functional-differential equations,” Lect. Notes Math., 243, 249–254 (1971).
P. O. Frederickson, “Global solutions to certain nonlinear functional differential equations,” J. Math. Anal. Appl., 33, 355–358 (1971).
G. P. Pelyukh and A. N. Sharkovskii, Introduction to the Theory of Functional Equations [in Russian], Naukova Dumka, Kiev (1974).
G. A. Derfel', “A probability method for the investigation of one class of functional differential equations,” Ukr. Mat. Zh., 41, No. 10, 1483–1491 (1989).
V. M. Polishchuk and A. N. Sharkovskii, “Representation of solutions of linear differential-difference equations of neutral type,” Differents. Uravn., 9, No. 9, 1627–1645 (1973).
D. V. Bel'skii, “On asymptotic properties of solutions of linear functional differential equations with constant coefficients and linearly transformed argument,” Nelin. Kolyvannya, 7, No. 1, 24–28 (2004).
B. G. Grebenshchikov and V. I. Rozhkov, “Asymptotic behavior of a solution of one stationary system with delay,” Differents. Uravn., 29, No. 5, 751–758 (1993).
B. G. Grebenshchikov and A. B. Lozhnikov, “Stabilization of a system containing a constant and linear delay,” Differents. Uravn., 40, No. 12, 1587–1595 (2004).
B. G. Grebenshchikov, “On asymptotic properties of some systems with two delays,” Izv. Vyssh. Uchebn. Zaved., Ser. Mat., 528, No. 5, 27–37 (2006).
G. P. Pelyukh and D. V. Bel'skii, “On asymptotic properties of solutions of functional differential equations with linearly transformed argument,” Nelin. Kolyvannya, 10, No. 1, 144–160 (2007).
I. Gumowski and C. Mira, Recurrences and Discrete Dynamic Systems, Springer, Berlin (1980).
J. Hale, Theory of Functional Differential Equations, Springer, New York (1977).
Author information
Authors and Affiliations
Additional information
__________
Translated from Neliniini Kolyvannya, Vol. 11, No. 2, pp. 147–150, April–June, 2008.
Rights and permissions
About this article
Cite this article
Bel’skii, D.V. On the asymptotic properties of solutions of linear functional differential equations with linearly transformed argument. Nonlinear Oscill 11, 153–157 (2008). https://doi.org/10.1007/s11072-008-0020-x
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s11072-008-0020-x