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Perturbations of Multipliers of Systems of Periodic Ordinary Differential Equations

Published online by Cambridge University Press:  03 June 2015

Leonid Berezansky ,
Michael Gil’  and
Liora Troib
Leonid Berezansky*
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
Michael Gil’*
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
Liora Troib*
Affiliation:
Department of Mathematics, Ben Gurion University of the Negev, P.O. Box 653, Beer-Sheva 84105, Israel
*
Corresponding author. URL: http://www.math.bgu.ac.il/brznsky/index.html Email: brznsky@cs.bgu.ac.il
Email: gilmi@cs.bgu.ac.il
Email: liora@cs.bgu.ac.il
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Abstract

The paper deals with periodic systems of ordinary differential equations (ODEs). A new approach to the investigation of variations of multipliers under perturbations is suggested. It enables us to establish explicit conditions for the stability and instability of perturbed systems.

Keywords

34D1034D20Periodic systemsperturbationsstabilityinstability
Type
Research Article
Information
Advances in Applied Mathematics and Mechanics , Volume 3 , Issue 5 , October 2011 , pp. 562 - 571
Copyright
Copyright © Global-Science Press 2011

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References

[1] BuŞe, C., Jitianu, O. and Preda, C., Exponential stability for solutions of linear differential equations with periodic coefficients, Int. J. Differ. Equ. Appl., 5 (2002), pp. 45–54.Google Scholar
[2] Daleckii, YU.L. and Krein, M. G., Stability of solutions of differential equations in Banach space, Am. Math. Soc., 1974.Google Scholar
[3] Giľ, M. I., Operator functions and localization of spectra, Lect. Notes Math., Vol. 1830, Springer Verlag, Berlin, 2003.Google Scholar
[4] Guseinov, G. and Kurpinar, E., On the stability of second order differential equations with periodic coefficients, J. Pure Appl. Math. Sci., 42(1-2) (1995), pp. 11–17.Google Scholar
[5] Halanay, A., Differential Equations: Stability, Oscillations, Time Lags, Academic Press, New York, 1966.Google Scholar
[6] Merman, G., Stability of some nonautonomous oscillatory canonical systems with a small parameter, Funct. Differ. Equ., 2 (1994), pp. 123–144.Google Scholar
[7] Saito, S. J. and Yamamoto, M., The continuous dependence of periodic solutions for the periodic quasilinear ordinary differential system containing a parameter, J. Math. Anal. Appl., 159(1) (1991), pp. 110–126.Google Scholar
[8] Sinha, S. C. and Butcher, E. A., Solution and stability of a set of p-th order linear differential equations with periodic coefficients via Chebyshev polynomials, Math. Probl. Eng., 2(2) (1996), pp. 165–190.Google Scholar
[9] Yakubovich, V. A. and Starzhinskii, V. M., Differential Equations with Periodic Coefficients, John Wiley, New York, 1975.Google Scholar
[10] Zevin, A. A., New approach to stability theory of linear canonical systems of differential equations with periodic coefficients, Prikl. Mat. Mekh., 68(2) (2004), pp. 206–224; translation in J. Appl. Math. Mech., 68(2) (2004), pp. 183–198.Google Scholar
[11] Zevin, A. A., Stability regions of linear canonical systems with periodic coefficients, J. Appl. Math. Mech., 62(1) (1998), pp. 37–42; translation from J. Prikl. Mat. Mekh., 62(1) (1998), pp. 41–48.Google Scholar