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 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz.: Year: Volume: Issue: Page: Find

 Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 2019, Volume 163, Pages 96–107 (Mi into454)

Lyapunov functions and asymptotics at infinity of solutions of equations that are close to Hamiltonian equations

O. A. Sultanov

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa

Abstract: We consider a nonlinear nonautonomous system of two ordinary differential equations with a stable fixed point and assume that the non-Hamiltonian part of the system tends to zero at infinity. We examine the asymptotic behavior of a two-parameter family of solutions that start from a neighborhood of the stable equilibrium. The proposed construction of asymptotic solutions is based on the averaging method and the transition in the original system to new dependent variables, one of which is the angle of the limit Hamiltonian system, and the other is the Lyapunov function for the complete system.

Keywords: nonlinear differential equation, asymptotics, averaging, Lyapunov function

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Bibliographic databases:
UDC: 517.928
MSC: 34E05, 34D05, 34D20

Citation: O. A. Sultanov, “Lyapunov functions and asymptotics at infinity of solutions of equations that are close to Hamiltonian equations”, Differential Equations, Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz., 163, VINITI, Moscow, 2019, 96–107

Citation in format AMSBIB
\Bibitem{Sul19} \by O.~A.~Sultanov \paper Lyapunov functions and asymptotics at infinity of solutions of equations that are close to Hamiltonian equations \inbook Differential Equations \serial Itogi Nauki i Tekhniki. Ser. Sovrem. Mat. Pril. Temat. Obz. \yr 2019 \vol 163 \pages 96--107 \publ VINITI \publaddr Moscow \mathnet{http://mi.mathnet.ru/into454} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=4014978}