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**Continuous dependence of the solution of a system of differential equations with impulses on the initial condition and a parameter in the presence of beating.**
*(English)*
Zbl 0651.34003

For systems of ordinary differential equations with impulses, the integral curve of the system may meet infinitely many times one and the same of previously fixed hypersurfaces on which the impulses are realized. This phenomenon is called beating. Sufficient conditions for the continuability of the solution of a system of differential equations with impulses in the presence of beating are found. Sufficient conditions for the continuous dependence of the solution on the initial conditions and a parameter are found without imposing conditions for the absence of beating.

### MSC:

34A12 | Initial value problems, existence, uniqueness, continuous dependence and continuation of solutions to ordinary differential equations |

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\textit{A. B. Dishliev} and \textit{D. D. Bainov}, Int. J. Syst. Sci. 19, No. 5, 669--685 (1988; Zbl 0651.34003)

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### References:

[1] | DOI: 10.1080/00036818408839511 · Zbl 0596.34016 |

[2] | FILATOV A. N., Averaging Methods in Differential and Integro-differential Equations (1971) · Zbl 0259.34002 |

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[4] | MIL’MAN V. D., Sib. math. J. 1 pp 64– (1960) |

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[6] | DOI: 10.1016/0022-247X(74)90174-7 · Zbl 0303.34042 |

[7] | SAMOILENKO A. M., Diff. Uravn. 13 pp 1981– (1977) |

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