Abstract
We obtain new nonimprovable conditions of oscillation of all solutions to a linear differential equation with several variable delays and positive coefficients. These conditions have the form of the upper and lower limits of the sum of integrals of the coefficients over the sets that are determined only by the delay corresponding to this coefficient. These results differ from the well-known results in which a coarsening of the integration set is assumed.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
References
R. G. Koplatadze and T. A. Chanturiya, “On oscillating and monotonic solutions to first-order differential equations with delayed arguments,” Differ. Uravn., 18, No. 8, 1463–1465 (1982).
A. D. Myshkis, “On solutions to first-order linear homogeneous differential equations of stable type with delayed argument,” Mat. Sb., 28, No. 3, 641–658 (1951).
M. I. Tramov, “Oscillation conditions for solutions to first-order differential equations with delayed argument,” Izv. Vyssh. Ucheb. Zaved. Ser. Mat., 3 (154), 92–96 (1975).
E. Braverman, G. E. Chatzarakis, and I. P. Stavroulakis, “Iterative oscillation tests for differential equations with several non-monotone arguments,” Adv. Difference Eqs., 87, 1–18 (2016).
K. Chudinov, “Note on oscillation conditions for first-order delay differential equations,” Electron. J. Qual. Theory Differ. Eqs., 2, 1–10 (2016).
N. Fukagai and T. Kusano, “Oscillation theory of first-order functional-differential equations with deviating arguments,” Ann. Mat. Pura Appl., 136, No. 4, 95–117 (1984).
I. Győri and G. Ladas, Oscillation Theory of Delay Differential Equations, Oxford Math. Monogr., New York (1991).
G. Infante, R. Koplatadze, and I. P. Stavroulakis, “Oscillation criteria for differential equations with several retarded arguments,” Funkcial. Ekvac., 58, No. 3, 347–364 (2015).
G. Ladas, V. Lakshmikantham, and J. S. Papadakis, “Oscillations of higher-order retarded differential equations generated by the retarded argument,” in: Proc. Conf. “Delay and Functional Differential Equations and Their Applications, Park City, Utah, 1972, Academic Press, New York (1972), pp. 219–231.
B. Li, “Oscillation of first-order delay differential equations,” Proc. Am. Math. Soc., 124, No. 12, 3729–3737 (1996).
X. H. Tang, “Oscillation of first-order delay differential equations with distributed delay,” J. Math. Anal. Appl., 289, No. 2, 367–378 (2004).
Author information
Authors and Affiliations
Corresponding author
Additional information
Translated from Itogi Nauki i Tekhniki, Seriya Sovremennaya Matematika i Ee Prilozheniya. Tematicheskie Obzory, Vol. 132, Proceedings of International Symposium “Differential Equations–2016,” Perm, 2016.
Rights and permissions
About this article
Cite this article
Chudinov, K.M. Exact Conditions of Oscillation of Solutions to Differential Equations with Several Delays. J Math Sci 230, 790–793 (2018). https://doi.org/10.1007/s10958-018-3791-3
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10958-018-3791-3