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Periodic solutions of nonlinear differential equations with pulse influence in a banach space

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Abstract

Rank conditions for control of linear pulse systems are established. An example of control synthesis in a problem for linear pulse systems is given.

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References

  1. A. M. Samoilenko and N. A. Perestyuk, “Periodic solutions of weakly nonlinear systems with pulse influence,”Differents. Uravn., No. 6, 1034–1045 (1978).

    Google Scholar 

  2. A. M. Samoilenko and N. A. Perestyuk, “Periodic and almost periodic solutions of differential equations with pulse influence,”Ukr. Mat. Zh.,34, No. 1, 66–73 (1982).

    Google Scholar 

  3. M. U. Akhmetov and N. A. Perestyuk, “Periodic and almost periodic solutions of systems with pulse influence,”Mat. Fiz., No. 34, 3–8 (1983).

    Google Scholar 

  4. V. E. Slyusarchuk, “Bounded solutions of pulse systems,”Differents. Uravn.,19, No. 4, 588–596 (1983).

    Google Scholar 

  5. V. E. Slyusarchuk, “Bounded solutions of systems close to pulse systems,”Dokl. Akad. Nauk Ukr.SSR, Ser. A, No. 8, 24–26 (1981).

    Google Scholar 

  6. V. E. Slyusarchuk, “Bounded solutions of pulse systems,” in:IX International Conference on Nonlinear Oscillations [in Russian], Vol. 2, Naukova Dumka, Kiev (1984), pp. 24–26.

    Google Scholar 

  7. A. M. Samoilenko and N. A. Perestyuk,Differential Equations with Pulse Influence [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  8. V. E. Slyusarchuk, “Weakly nonlinear perturbations of pulse systems,”Mat. Fiz. Nelinein. Mekh.,49, No. 15, 48–56 (1991).

    Google Scholar 

  9. A. M. Samoilenko, Yu. V. Teplinskii, and V. E. Luchik, “Reducibility of differential equations with pulses in the space of bounded number sequences,”Dokl. Akad. Nauk Ukr.SSR, Ser. A, No. 5, 27–30 (1990).

    Google Scholar 

  10. V. E. Slyusarchuk, “On exponential dichotomy of solutions to pulse systems,”Ukr. Mat. Zh.,41, No. 6, 779–783 (1989).

    Google Scholar 

  11. V. I. Gutsu, “Periodic solutions of linear differential equations with pulses in Banach space,” in:Differents. Uravn. Mat. Fiz., Kishinev (1989), pp. 59–66.

  12. A. M. Samoilenko and M. Ilolov, “Inhomogeneous evolutionary equations with pulse influence,”Ukr. Mat. Zh.,44, No. 1, 93–100 (1992).

    Google Scholar 

  13. Yu. V. Rogovchenko and S. I. Trofimchuk,Periodic Solutions of Weakly Nonlinear Partial Differential Equations of Parabolic Type with Pulse Influence and Their Stability [in Russian], Preprint, No. 86.65, Institute of Mathematics, Ukrainian Academy of Sciences, Kiev (1986).

    Google Scholar 

  14. D. D. Bainov, S. I. Kostadinov, and A. D. Myshkis, “Bounded and periodic solutions of differential equations with impulse effect in a Banach space,”Diff. Integral Equations,1, No. 2, 223–230 (1988).

    Google Scholar 

  15. A. F. Filippov,Differential Equations with Discontinuous Right-Hand Side [in Russian], Nauka, Moscow (1985).

    Google Scholar 

  16. Discontinuous Dynamical Systems (Abstracts of Papers on the Conference in Ivano-Frankovsk), Kiev (1990).

  17. Discontinuous Dynamical Systems (Abstracts of Papers on the Seminar-Conference in Uzhgorod), Kiev (1991).

  18. A. N. Kolmogorov and S. V. Fomin,Elements of the Theory of Functions and Functional Analysis [in Russian], Nauka, Moscow (1968).

    Google Scholar 

  19. R. Edwards,Functional Analysis [Russian translation], Mir, Moscow (1969).

    Google Scholar 

  20. S. G. Krein,Linear Equations in Banach Spaces [in Russian], Nauka, Moscow (1971).

    Google Scholar 

  21. Yu. L. Daletskii and M. G. Krein,Stability of Solutions of Differential Equations in Banach Spaces [in Russian], Nauka, Moscow (1970).

    Google Scholar 

  22. T. Kato,Theory of Perturbations of Linear Operators [Russian translation], Mir, Moscow (1972).

    Google Scholar 

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Published in Ukrainskii Matematicheskii Zhurnal, Vol. 47, No. 3, pp. 370–380, March, 1995.

This work was partially supported by the Ukrainian State Committee on Science and Technology.

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Perestyuk, N.A., Slyusarchuk, V.E. Periodic solutions of nonlinear differential equations with pulse influence in a banach space. Ukr Math J 47, 430–442 (1995). https://doi.org/10.1007/BF01056305

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  • DOI: https://doi.org/10.1007/BF01056305

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