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Forced oscillations of an infinite-dimensional oscillator under impulsive perturbations

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Abstract

We establish existence and uniqueness theorems for the impulsive operator differential equation {fx177-01}. The operator A can be noninvertible. The obtained results are applied to differential-algebraic equations and partial differential equations of the non-Kovalevskaya type.

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References

  1. A. M. Samoilenko and T. G. Strizhak, “On the motion of an oscillator under the action of instantaneous force,” in: Proceedings of the Seminar on Mathematical Physics and Nonlinear Oscillations [in Russian], Issue 4, Kiev (1968), pp. 213–218.

  2. A. M. Samoilenko and N. A. Perestyuk, Impulsive Differential Equations [in Russian], Vyshcha Shkola, Kiev (1987).

    Google Scholar 

  3. Yu. A. Mitropol'skii and A. A. Molchanov, Computer Analysis of Nonlinear Resonance Circuits [in Russian], Naukova Dumka, Kiev (1981).

    Google Scholar 

  4. S. L. Sobolev, “Cauchy problem for a special case of systems of non-Kovalevskaya type,” Dokl. Akad. Nauk SSSR, 82, No. 2, 205–208 (1952).

    MATH  MathSciNet  Google Scholar 

  5. H. O. Fattorini, Second-Order Linear Differential Equations in Banach Spaces, North-Holland (1985).

  6. A. Rutkas and L. Vlasenko, “Implicit operator differential equations and applications to electrodynamics,” Math. Meth. Appl. Sci., 23, No. 1, 1–15 (2000).

    Article  MATH  MathSciNet  Google Scholar 

  7. L. A. Vlasenko, Evolution Models with Implicit and Degenerate Differential Equations [in Russian], Sistemnye Tekhnologii, Dnepropetrovsk (2006).

    Google Scholar 

  8. A. D. Myshkis and A. M. Samoilenko, “Systems with pulses at given times,” Mat. Sb., 74, No. 2, 202–208 (1967).

    MathSciNet  Google Scholar 

  9. A. G. Rutkas, “Cauchy problem for the equation Ax′(t) + Bx(t) = f(t),” Differents. Uravn., 11, No. 11, 1996–2010 (1975).

    MATH  MathSciNet  Google Scholar 

  10. J.-L. Lions and E. Magenes, Problémes aux Limites non Homogénes et Applications, Dunod, Paris (1968).

    MATH  Google Scholar 

  11. H. Gajewski, K. Gröger, and K. Zacharias, Nichtlineare Operatorgleichungen und Operatordifferentialgleichungen, Akademie, Berlin (1974).

    MATH  Google Scholar 

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

    MathSciNet  Google Scholar 

  13. A. G. Rutkas and L. A. Vlasenko, “Existence, uniqueness, and continuous dependence for implicit semilinear functional differential equations,” Nonlin. Anal. TMA, 55, No. 1–2, 125–139 (2003).

    Article  MATH  MathSciNet  Google Scholar 

  14. A. M. Samoilenko, M. I. Shkil', and V. P. Yakovets', Linear Systems of Degenerate Differential Equations [in Ukrainian], Vyshcha Shkola, Kyiv (2000).

    Google Scholar 

  15. L. A. Vlasenko, “Degenerate time-dependent neutral functional differential equations in Banach spaces,” Funct. Different. Equat., 14, No. 2–4, 423–438 (2007).

    MATH  MathSciNet  Google Scholar 

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Translated from Ukrains'kyi Matematychnyi Zhurnal, Vol. 60, No. 2, pp. 155–166, February, 2008.

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Vlasenko, L.A. Forced oscillations of an infinite-dimensional oscillator under impulsive perturbations. Ukr Math J 60, 177–190 (2008). https://doi.org/10.1007/s11253-008-0050-7

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  • DOI: https://doi.org/10.1007/s11253-008-0050-7

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