Journal of Applied Mathematics and Mechanics (about journal) Journal of Applied
Mathematics and Mechanics

Russian Academy of Sciences
 Founded
in January 1936
(Translated from 1958)
Issued 6 times a year
ISSN 0021-8928
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V.V. Kozlov, "Remarks on the degree of instability," J. Appl. Math. Mech. 74 (1), 10-12 (2010)
Year 2010 Volume 74 Issue 1 Pages 10-12
Title Remarks on the degree of instability
Author(s) V.V. Kozlov (Moscow, Russia, kozlov@pran.ru)
Abstract Linear systems of differential equations allowing of functions in quadratic forms that do not increase along trajectories with time are considered. The relations between the indices of inertia of these forms and the degrees of instability of equilibrium states are indicated. These assertions generalize known results from the oscillation theory of linear systems with dissipation, and reveal the mechanism of loss of stability when non-increasing quadratic forms lose the property of a minimum.
Received 20 January 2009
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