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 readings-2007), Minsk, May 16-19, 2007 - Minsk, Institute of mathematics of NAS of Belarus, 2007. P. 191-198. [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.