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Asymptotic solutions of singularly perturbed nonlinear systems of impulsive differential equations with degeneration

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References

  1. Vasil’eva, A.B. and Butuzov, V.F., Asimptoticheskie razlozheniya reshenii singulyarno vozmushchennykh uravnenii (Asymptotic Expansions of the Solutions of Singularly Perturbed Equations), Moscow: Nauka, 1973.

    Google Scholar 

  2. Samoilenko, A.M. and Perestyuk, N.A., Differentsial’nye uravneniya s impul’snym vozdeistviem (Impulsive Differential Equations), Kiev: Vyshcha Shkola, 1987.

    Google Scholar 

  3. Samoylenko, V.Hr. and Elgondyev, K.K., Ukrain. Mat. Zh., 1997, vol. 49, no. 1, pp. 140–147.

    Google Scholar 

  4. Elgondyev, K.K., Uzbek. Mat. Zh., 1997, no. 4, pp. 62–67.

  5. Samoylenko, V.Hr. and Elgondyev, K.K., Differ. Uravn., 1999, vol. 35, no. 6, p. 852.

    Google Scholar 

  6. Butuzov, V.F. and Urazgil’dina, T.A., Ukrain. Mat. Zh., 1987, vol. 39, no. 1, pp. 13–21.

    MATH  MathSciNet  Google Scholar 

  7. Velizhanina, K.A., Vozhukova, E.A., and Nefedov, N.N., Akust. Zh., 1986, vol. 32, no. 1, pp. 114–116.

    Google Scholar 

  8. Samoilenko, A.M., Boichuk, A.A., and Karandzhulov, L.I., Differ. Uravn., 2001, vol. 37, no. 9, pp. 1186–1193.

    MathSciNet  Google Scholar 

  9. Samoilenko, A.M., Kaplun, Yu.I., and Samoylenko, V.Hr., Ukrain. Mat. Zh., 2002, vol. 54, no. 8, pp. 1089–1099.

    MathSciNet  Google Scholar 

  10. Samoilenko, A.M., Shkil’, M.I., and Yakovets, V.P., Liniini sistemy dyferentsial’nykh rivnyan’ z vyrodzhennyamy (Linear Systems of Differential Equations with Degeneration), Kiev: Vyshcha Shkola, 2000.

    Google Scholar 

  11. Shkil’, M.I., Starun, I.I., and Yakovets, V.P., Asimptoticheskoe integrirovanie lineinykh sistem differentsial’nykh uravnenii s vyrozhdeniem (Asymptotic Integration of Linear Systems of Differential Equations with Degeneration), Kiev: Vyshcha Shkola, 1991.

    Google Scholar 

  12. Bellman, R., Introduction to Matrix Analysis, New York: McGraw-Hill Book Co., 1960. Translated under the title Vvedenie v teoriyu matrits, Moscow: Nauka, 1969.

    MATH  Google Scholar 

  13. Krivosheya, S.O., Bugrin, M.A., and Perestyuk, N.A., Differentsial’nye i integral’nye uravneniya (Differential and Integral Equations), Kiev, 2004.

  14. Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988.

    MATH  Google Scholar 

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Original Russian Text © V.V. Potorocha, V.Hr. Samoylenko, 2007, published in Differentsial’nye Uravneniya, 2007, Vol. 43, No. 3, pp. 324–334.

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Potorocha, V.V., Samoylenko, V.H. Asymptotic solutions of singularly perturbed nonlinear systems of impulsive differential equations with degeneration. Diff Equat 43, 334–345 (2007). https://doi.org/10.1134/S0012266107030044

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  • DOI: https://doi.org/10.1134/S0012266107030044

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