References
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.
Samoilenko, A.M. and Perestyuk, N.A., Differentsial’nye uravneniya s impul’snym vozdeistviem (Impulsive Differential Equations), Kiev: Vyshcha Shkola, 1987.
Samoylenko, V.Hr. and Elgondyev, K.K., Ukrain. Mat. Zh., 1997, vol. 49, no. 1, pp. 140–147.
Elgondyev, K.K., Uzbek. Mat. Zh., 1997, no. 4, pp. 62–67.
Samoylenko, V.Hr. and Elgondyev, K.K., Differ. Uravn., 1999, vol. 35, no. 6, p. 852.
Butuzov, V.F. and Urazgil’dina, T.A., Ukrain. Mat. Zh., 1987, vol. 39, no. 1, pp. 13–21.
Velizhanina, K.A., Vozhukova, E.A., and Nefedov, N.N., Akust. Zh., 1986, vol. 32, no. 1, pp. 114–116.
Samoilenko, A.M., Boichuk, A.A., and Karandzhulov, L.I., Differ. Uravn., 2001, vol. 37, no. 9, pp. 1186–1193.
Samoilenko, A.M., Kaplun, Yu.I., and Samoylenko, V.Hr., Ukrain. Mat. Zh., 2002, vol. 54, no. 8, pp. 1089–1099.
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.
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.
Bellman, R., Introduction to Matrix Analysis, New York: McGraw-Hill Book Co., 1960. Translated under the title Vvedenie v teoriyu matrits, Moscow: Nauka, 1969.
Krivosheya, S.O., Bugrin, M.A., and Perestyuk, N.A., Differentsial’nye i integral’nye uravneniya (Differential and Integral Equations), Kiev, 2004.
Gantmakher, F.R., Teoriya matrits (Theory of Matrices), Moscow: Nauka, 1988.
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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