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Boundary value problem for a singularly perturbed system of linear differential equations with impulses

Published online by Cambridge University Press:  20 January 2009

D. D. Bainov ,
M. A. Hekimova  and
V. M. Veliov
D. D. Bainov
Affiliation:
Department of MathematicsUniversity of PlovdivPlovdiv, Bulgaria
M. A. Hekimova
Affiliation:
Department of MathematicsUniversity of PlovdivPlovdiv, Bulgaria
V. M. Veliov
Affiliation:
Institute of MathematicsBulgarian Academy of Sciences1090 SofiaP.O. Box 373, Bulgaria
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In connection with the analysis of mathematical models of real processes undergoing short time perturbations, in the last years the interest in the differential equations with impulses remarkably increased. Going back to the papers of Mil'man and Myshkis [4, 5] the investigations of this subject are now extended to different directions concerning applications in physics, biology, electronics, automatic control etc.

Type
Research Article
Information
Proceedings of the Edinburgh Mathematical Society , Volume 31 , Issue 1 , February 1988 , pp. 107 - 126
Copyright
Copyright © Edinburgh Mathematical Society 1988

References

REFERENCES

1.Flato, L. and Levinson, N., Periodic solutions of singularly perturbed systems, J. Rat. Mech. Anal. 4 (1953), 943–950.Google Scholar
2.Hekimova, M. A. and Bainov, D. D., Periodic solutions of singularly perturbed systems of differential equations with impulse effect, ZAMP 36 (1985), 520–537.Google Scholar
3.Kokotovic, P. V., Applications of singular perturbation techniques to control problems, SIAM Rev. 26 (1984), 501–550.CrossRefGoogle Scholar
4.Mil'man, V. D. and Myshkis, A. D., On the stability of motion in presence of impulses, Siberian Math. J. 1 (1960), 233–237 (in Russian).Google Scholar
5.Mil'man, V. D. and Myshkis, A. D., Random impulses in linear dynamic systems, in Asymptotic Methods for Solving Differential Equations (Ed. AN UkSSR, Kiev, 1963), 64–81 (in Russian).Google Scholar
6.Tihonov, A. N., Systems of differential equations containing a small parameter multiplying the derivative, Mat. Sb. 31(73) (1952), 575–586.Google Scholar
7.Vasileva, A. B. and Butuzov, V. F., Asymptotic Expansions of Solutions of Singularly Perturbed Systems of Differential Equations (Nauka, Moscow, 1973) (in Russian).Google Scholar