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Investigation of Systems of Differential Equations with Delays and Constraints Imposed on the Derivatives of Solutions

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Ukrainian Mathematical Journal Aims and scope

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

  1. A. D. Myshkis, Linear Differential Equations with Delayed Argument [in Russian], Gostekhizdat, Moscow (1951).

    Google Scholar 

  2. 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).

    Google Scholar 

  3. A. D. Myshkis, “On some problems of the theory of differential equations with deviating argument,” Usp. Mat. Nauk, 32, No. 2, 173–202 (1977).

    MathSciNet  Google Scholar 

  4. E. Pinney, Ordinary Difference-Differential Equations, University of California, Berkeley (1958).

    MATH  Google Scholar 

  5. R. Bellman and K. L. Cooke, Differential-Difference Equations, Academic Press, New York (1963).

    MATH  Google Scholar 

  6. V. P. Rubanik, Oscillations of Quasilinear Systems with Delay [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  7. L. É. Él’sgol’ts and S. B. Norkin, Introduction to the Theory of Differential Equations with Deviating Argument [in Russian], Nauka, Moscow (1971).

    MATH  Google Scholar 

  8. J. Hale, Theory of Functional Differential Equations, Springer, New York (1977).

    Book  Google Scholar 

  9. E. F. Tsar’kov, Random Perturbations of Functional-Differential Equations [in Russian], Zinatne, Riga (1989).

    MATH  Google Scholar 

  10. N. V. Azbelev, V. P. Maksimov, and L. F. Rakhmatullina, Introduction to the Theory of Functional-Differential Equations [in Russian], Moscow, Nauka (1991).

    MATH  Google Scholar 

  11. 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).

    Google Scholar 

  12. 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).

  13. 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).

    Article  MathSciNet  Google Scholar 

  14. S. M. Kopeikin and É. Fomalont, “Fundamental limit of the velocity of gravitation and its measurements,” Zemlya Vselennaya, No. 3 (2004).

  15. G. M. Fikhtengol’ts, A Course of Differential and Integral Calculus [in Russian], Vol. 1, Nauka, Moscow (1966).

    Google Scholar 

  16. V. A. Zorich, Mathematical Analysis [in Russian], Vol. 2, Nauka, Moscow (1984).

    Google Scholar 

  17. A. B. Antonevich and Ya. V. Radyno, Functional Analysis and Integral Equations [in Russian], Universitetskoe Izd., Minsk (1984).

    MATH  Google Scholar 

  18. A. N. Kolmogorov and S. V. Fomin, Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1972).

    Google Scholar 

  19. L. Nirenberg, Topics in Nonlinear Functional Analysis [Russian translation], Mir, Moscow (1977).

    Google Scholar 

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Correspondence to V. Yu. Slyusarchuk.

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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

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