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Justification of the averaging method for a system of singularly perturbed differential equations with impulses

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Abstract

The averaging method is justified for a system of singularly perturbed differential equations of the form

$$\dot x(t) = X\left( {t,\frac{t}{\varepsilon },x(t),y(t),\varepsilon } \right),\varepsilon \dot y(t) = Y(t,x(t),y(t))$$

, in the presence of impulses.

Zusammenfassung

Gegenstand dieser Arbeit ist die mathematische Begründung einer Mittelungsmethode für eine Klasse singulär gestörter gewöhnlicher Differentialgleichungen die überdies Unstetigkeiten aufweisen.

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References

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Authors and Affiliations

  1. Higher Institute of Mechanical and Electrical Engineering, Sofia

    S. D. Milusheva

  2. University of Plovdiv, Bulgaria

    D. D. Bainov

Authors
  1. S. D. Milusheva
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  2. D. D. Bainov
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Milusheva, S.D., Bainov, D.D. Justification of the averaging method for a system of singularly perturbed differential equations with impulses. Z. angew. Math. Phys. 36, 293–308 (1985). https://doi.org/10.1007/BF00945463

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  • DOI: https://doi.org/10.1007/BF00945463

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