We establish conditions for the existence and uniqueness of the solutions to nonlinear systems of differential equations with delays and restrictions imposed on the delays and derivatives of the solutions.
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References
A. D. Myshkis, Linear Differential Equations with Delayed Argument [in Russian], Gostekhizdat, Moscow (1951).
A. D. Myshkis and L. É. Él’sgol’ts, “State and problems of the theory of differential equations with deviating argument,” Usp. Mat. Nauk, 22, No. 2, 21–57 (1967).
A. D. Myshkis, “On some problems of the theory of differential equations with deviating argument,” Usp. Mat. Nauk, 32, No. 2, 173–202 (1977).
E. Pinney, Ordinary Difference-Differential Equations, University of California, Berkeley (1958).
R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York (1963).
V. P. Rubanik, Oscillations of Quasilinear Systems with Delay [in Russian], Nauka, Moscow (1971).
L. É. Él’sgol’ts and S. B. Norkin, Introduction to the Theory of Differential Equations with Deviating Argument [in Russian], Nauka, Moscow (1971).
J. Hale, Theory of Functional Differential Equations, Springer, New York (1977).
E. F. Tsar’kov, Random Perturbations of Functional-Differential Equations [in Russian], Zinatne, Riga (1989).
N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional-Differential Equations [in Russian], Moscow, Nauka (1991).
V. Yu. Slyusarchuk, Absolute Stability of Dynamical Systems with Aftereffect [in Ukrainian], Rivne State University of Water Management and Utilization of Natural Resources, Rivne (2003).
V. Yu. Slyusarchuk, “Mathematical model of the Solar system with account of gravitational velocity,” Nelin. Kolyv., 21, No. 2, 238–261 (2018); English translation:J. Math. Sci., 243, No. 2, 287–312 (2018).
V. Yu. Slyusarchuk, “Non-Keplerian behavior and instability of motion of two bodies caused by the finite velocity of gravitation,” Nelin. Kolyv., 21, No. 3, 397–419 (2018); English translation:J. Math. Sci., 243, No. 3, 467–492 (2018).
S. M. Kopeikin and É. Fomalont, “Fundamental limit of the velocity of gravitation and its measurements,” Zemlya Vselennaya, No. 3 (2004).
G. M. Fikhtengol’ts, A Course of Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1966).
V. A. Zorich, Mathematical Analysis [in Russian], Vol. 2, Nauka, Moscow (1984).
A. B. Antonevich and Ya. V. Radyno, Functional Analysis and Integral Equations [in Russian], Universitetskoe Izd., Minsk (1984).
A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1972).
L. Nirenberg, Topics in Nonlinear Functional Analysis [Russian translation], Mir, Moscow (1977).
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Translated from Ukrains’kyi Matematychnyi Zhurnal, Vol. 71, No. 5, pp. 677–691, May, 2019.
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Slyusarchuk, V.Y. Investigation of Systems of Differential Equations with Delays and Constraints Imposed on the Derivatives of Solutions. Ukr Math J 71, 774–791 (2019). https://doi.org/10.1007/s11253-019-01673-0
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DOI: https://doi.org/10.1007/s11253-019-01673-0