Geodesic
Asymptotic quiescent position for systems of homogeneous non-autonomous differential equations
Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2014), pp. 58-65

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A system of homogeneous non-autonomous differential equations with disturbed right-hand parts is considered. The zero solution doesn’t exist for the considered system but the question about behavior of solutions starting near zero is still open. Conditions for existing of asymptotic quiescent position are determined if the right parts of the system satisfies provided conditions. A corresponding theorem is proved based on second Lyapunov method which allows to use the provided function for further researches. In conclusion an illustrative example is given which avows obtained results. Bibliogr. 5. Il. 1.
Keywords: asymptotic quiescent position, asymptotic stability, non-autonomous differential equations, homogeneous differential equation, uniform average. 
O. G. Tikhomirov; E. V. Temkina. Asymptotic quiescent position for systems of homogeneous non-autonomous differential equations. Vestnik Sankt-Peterburgskogo universiteta. Prikladnaâ matematika, informatika, processy upravleniâ, no. 3 (2014), pp. 58-65. http://geodesic.mathdoc.fr/item/VSPUI_2014_3_a5/
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