Ukrainian Mathematical Congress  2009
Vladimir Alexeevich Chiricalov (Taras Shevchenko national university of Kyiv, Ukraine) Monodromy operator of matrix impulsive periodic differential equation and localization of its spectral set
In our report we consider angular and radial locali
zation of eigenvalues of monodromy operator of impulsive matrix periodic differential equations. We use M.G.Krein\'s
rezults which reprezented in monograph [1].In the paper [2] representation of evolution operator in the form of
multiplicative Stiltjes integral has been obtained. Using Krein\'s estimation of angular deviation of multiplicative
integral and Kantorovich formula for matrix exponent the estimations of angular deviation of monodromy operator impulsive
matrix periodic differential equation have been obtained.
[1]Daletskiy Yu.L.,Krein M.G. Stability of solutions of differential equations in Banach space. Moscow, Nauka, 1970 (in
Russian).
[2]Chiricalov V.A. Matrix impulsive periodic differential equation of the second order.In: Proceedings of XII Int. Conf.
of Differential equations (Erugin readings2007), Minsk, May 1619, 2007  Minsk, Institute of mathematics of NAS of
Belarus, 2007. P. 191198.
[3]Chiricalov V.A.Periodic solutions of difference matrix equations./Analytic Methods of Analysis and Differential
Equations (AMADE  2006)}: Proceedings of conference. Editors: A.A. Kilbas and S.V. Rogosin., Cambridge: Cambridge
Scientific Publishers, 2007, pp. 45  54.
