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General Theorems on the Existence and Uniqueness of Solutions of Impulsive Differential Equations

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Abstract

We study the Cauchy problem for impulsive differential equations in the general case.

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REFERENCES

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

    Google Scholar 

  2. A. Halanay and D. Wexler, Qualitative Theory of Pulse Systems [Russian translation], Mir, Moscow (1971).

    Google Scholar 

  3. P. C. Das and R. R. Sharma, “Existence and stability of measure differential equations,” Czech. Math. J., 22, No.97, 145–158 (1972).

    Google Scholar 

  4. S. Schwabik, Generalized Differential Equations. Fundamental Results, Rozpr. ČSAV MPV, Prague (1985).

    Google Scholar 

  5. S. Schwabik, Generalized Differential Equations. Special Results, Rozpr. ČSAV MPV, Prague (1989).

    Google Scholar 

  6. S. I. Trofimchuk, Investigation of Almost Periodic Pulse Systems [in Russian], Doctoral-Degree Thesis (Physics and Mathematics), Kiev (1993).

  7. R. M. Tatsii, Discrete-Continuous Boundary-Value Problems for Differential Equations with Measures [in Russian], Doctoral-Degree Thesis, Lvov (1994).

  8. G. E. Shilov, Mathematical Analysis. A Special Course [in Russian], Fizmatgiz, Moscow (1960).

    Google Scholar 

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

    Google Scholar 

  10. V. E. Slyusarchuk, “On one property of absolutely convergent number series,” in: A. Ya. Dorogovtsev (editor), Mathematics Today'97 [in Russian], TViMS, Kiev (1997), pp. 28–42.

    Google Scholar 

  11. V. E. Slyusarchuk, “Weakly nonlinear perturbations of pulse systems,” Mat. Fiz. Nelin. Mekh., 215(49), 32–35 (1991).

    Google Scholar 

  12. V. E. Slyusarchuk, “P-continuous operators and their application to the solution of problems of mathematical physics,” Integr. Peretv. Zastos. Kraiov. Zadach, No. 15, 188–226 (1997).

    Google Scholar 

  13. T. Kato, Perturbation Theory for Linear Operators [Russian translation], Mir, Moscow (1972).

    Google Scholar 

  14. M. A. Krasnosel'skii, Positive Solutions of Operator Equations [in Russian], Fizmatgiz, Moscow (1962).

    Google Scholar 

  15. S. A. Chaplygin, “A new method for approximate integration of differential equations,” Tr. Tsentr. Aérodinam. Inst., No. 130, 5–17 (1932).

    Google Scholar 

  16. A. M. Samoilenko and S. D. Borisenko, “Sum-integral inequalities and stability of processes with discrete perturbations,” in: Differential Equations and Their Applications. Proceedings of the Third International Conference, Vol. 1, Russe (Bulgaria) (1987), pp. 377–380.

    Google Scholar 

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Authors and Affiliations

  1. Rivne Technical University, Rivne

    V. E. Slyusarchuk

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  1. V. E. Slyusarchuk
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Slyusarchuk, V.E. General Theorems on the Existence and Uniqueness of Solutions of Impulsive Differential Equations. Ukrainian Mathematical Journal 52, 1094–1106 (2000). https://doi.org/10.1023/A:1005281717641

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