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Periodic solutions of quasilinear impulse systems in the critical case

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Abstract

Conditions for the existence of periodic solutions of weakly-nonlinear autonomous and nonautonomous impulse systems in the critical case are determined.

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Literature cited

  1. N. M. Krylov and N. N. Bogolyubov, Introduction to Nonlinear Mechanics [in Russian], Izd. Akad. Nauk Ukr. SSR, Kiev (1937).

    Google Scholar 

  2. Yu. A. Mitropol'skii, The Averaging Method in Nonlinear Mechanics [in Russian], Naukova Dumka, Kiev (1977).

    Google Scholar 

  3. A. M. Samoilenko and N. A. Perestyuk, Differential Equations with Impulse Action [in Russian], Vishcha Shkola, Kiev (1987).

    Google Scholar 

  4. I. G. Malkin, Some Problems of the Theory of Nonlinear Oscillations [in Russian], Gostekhizdat, Moscow (1956).

    Google Scholar 

  5. M. U. Akhmetov and N. A. Perestyuk, “On the motion with impulse action on surfaces,” Izv. Akad. Nauk Kazakh. SSR, No. 1, 11–14 (1988).

    Google Scholar 

  6. M. U. Akhmetov and N. A. Perestyuk, “Periodic solutions of differential equations with impulse action on surfaces,” in: Application of Asymptotic Methods in the Theory of Nonlinear Oscillations [in Russian], Inst. Mat. Akad. Nauk Ukrain. SSR, Kiev (1987). pp. 11–14.

    Google Scholar 

  7. M. U. Akhmetov and N. A. Perestyuk, “On the differentiable dependence of the solutions of impulse systems on initial data,” Ukr. Mat. Zh.,41, No. 8, 1028–1033 (1989).

    Google Scholar 

  8. M. U. Akhmetov and N. A. Perestyuk, “Stability of periodic solutions of systems of differential equations with impulse action on surfaces,” Ukr. Mat. Zh.,41, No. 12, 1596–1604 (1989).

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Translated from Ukrainskii Matematicheskii Zhurnal, Vol. 43, No. 3, pp. 308–315, March, 1991.

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Akhmetov, M.U., Perestyuk, N.A. Periodic solutions of quasilinear impulse systems in the critical case. Ukr Math J 43, 273–279 (1991). https://doi.org/10.1007/BF01670065

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  • DOI: https://doi.org/10.1007/BF01670065

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