Abstract
We consider a class of autonomous functional-differential equations for which the properties of oscillation of all solutions and positiveness of the fundamental solution are mutually complementary.
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N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Linear Functional Differential Equations, World Federation Publ., Atlanta (1995).
A. S. Balandin, “On the positiveness of the fundamental solution of linear autonomous differentialdifference equations with coefficients of opposite signs,” in: Proc. Int. Conf. “Modern Problems of Applied mathematics, Control Theory, and Computer Science, 2014” [in Russian], Voronezh (2014), pp. 22–25.
R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York–London (1963).
V. V. Malygina, “On the construction of the domain of oscillation for autonomous differential equations with delay,” in: Proc. Int. Conf. “Modern Problems of Applied mathematics, Control Theory, and Computer Science, 2015” [in Russian], Voronezh (2015), pp. 223–225.
A. D. Myshkis, Linear Differential Equations with Delayed Arguments [in Russian], Nauka, Moscow (1972).
T. L. Sabatulina, “On oscillating solutions of one nonautonomous differential equation with delay,” in: Proc. Int. Conf. “Modern Problems of Applied mathematics, Control Theory, and Computer Science, 2015” [in Russian], Voronezh (2015), pp. 314–315.
M. I. Tramov, “Conditions of oscillation of solutions to first-order differential equations with delayed argument,” Izv. Vyssh. Ucheb. Zaved. Ser. Mat., 3, 92–96 (1975).
J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York–Heidelberg–Berlin (1977).
S. A. Chaplygin, A new method of approximate integration of differential equations [in Russian], Gostekhizdat, Moscow–Leningrad (1950).
I. Győri and G. Ladas, Oscillation Theory of Delay Differential Equations with Applications, The Clarendon Press and Oxford Univ. Press, New York (1991).
T. Sabatulina and V. Malygina, “On positiveness of the fundamental solution for a linear autonomous differential equation with distributed delay,” Electron. J. Qual. Theory Differ. Equ., 61, 1–16 (2014).
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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.
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Sabatulina, T.L. Oscillating and Sign-Definite Solutions to Autonomous Functional-Differential Equations. J Math Sci 230, 766–769 (2018). https://doi.org/10.1007/s10958-018-3786-0
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DOI: https://doi.org/10.1007/s10958-018-3786-0