Hostname: page-component-848d4c4894-75dct Total loading time: 0 Render date: 2024-05-23T18:51:53.796Z Has data issue: false hasContentIssue false
  • English
  • Français

Periodic solutions of quasilinear non-autonomous systems with impulses

Published online by Cambridge University Press:  17 April 2009

S.G. Hristova  and
D.D. Bainov
S.G. Hristova
Affiliation:
23 Oborishte Str., 1504 Sofia, Bulgaria.
D.D. Bainov
Affiliation:
23 Oborishte Str., 1504 Sofia, Bulgaria.
Rights & Permissions [Opens in a new window]

Abstract

Core share and HTML view are not available for this content. However, as you have access to this content, a full PDF is available via the ‘Save PDF’ action button.

The paper considers a system of differential equations with impulse perturbations at fixed moments in time of the form

where x ∈ Rn, ε is a small parameter,

Sufficient conditions are found for the existence of the periodic solution of the given system in the critical and non-critical cases.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 31 , Issue 2 , April 1985 , pp. 185 - 197
Copyright
Copyright © Australian Mathematical Society 1985

References

[1]Halanai, A. and Vexler, D., Qualitative theory of impulse systems (MIR, 1971).Google Scholar
[2]Millman, V.D. and Mishkis, A.D., “On stability of motion in the presence of impulse perturbations”, Sibirsk. Mat. Ž. 1 (1960), 233–237 (in Russian).Google Scholar
[3]Millman, V.D. and Mishkis, A.D., “Random impulse perturbations in linear dynamic systems”, Approximate methods for the solution of differential equations, 64–81 (Publishing House of the Acad. Sci. Ukrain. SSR, Kiev, 1963).Google Scholar
[4]Pandit, S.G., “On the stability of impulsively perturbed differential systems”, Bull. Austral. Math. Soc. 17 (1977), 423–432.CrossRefGoogle Scholar
[5]Pandit, S.G., “Differential systems with impulsive perturbations”, Pacific J. Math. 86 (1980), 553–560.CrossRefGoogle Scholar
[6]Pandit, S.G., “Systems described by differential equations containing impulses: existence, and uniqueness”, Rev. Roumaine Math. Pures Appl. 26 (1981), 879–887.Google Scholar
[7]Pandit, S.G. and Deo, S.G., Differential equations with impulses (Springer-Verlag, Berlin, Heidelberg, New York, 1982).Google Scholar
[8]Pavlidis, T., “Stability of systems described by differential equations containing impulses”, IEEE Trans. Automat. Control. 12 (1967), 43–45.CrossRefGoogle Scholar
[9]Raghavendra, V. and Mohana Rao, M. Rama, “On the stability of differential systems with respect to impulsive perturbations”, J. Math. Anal. Appl. 48 (1974), 515–526.CrossRefGoogle Scholar
[10]Hari Rao, V. Sree, “On boundedness of impulsively perturbed systems”, Bull. Austral. Math. Soc. 18 (1978), 237–242.Google Scholar
[11]Mohana Rao, M. Rama and Hari Rao, V. Sree, “Stability of impulsively perturbed systems”, Bull. Austral. Math. Soc. 16 (1977), 99–110.CrossRefGoogle Scholar
[12]Samoilenko, A.M. and Perestiuk, N.A., “Periodic and almost periodic solutions of differential equations with impulse perturbations”, Ukrain. Mat. Ž. 34 (1982), 66–73.Google Scholar