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Mat. Zametki, 2015, Volume 98, Issue 5, Pages 695–709 (Mi mz10667)  

Lyapunov Functions in Justification Theorems for Asymptotics

L. A. Kalyakin

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

Abstract: A formal asymptotic solution is considered for a nonlinear system of ordinary differential equations in a neighborhood of a singular point. The problem of existence of an exact solution with such an asymptotics and the problem of stability of this solution are solved. The main tool in these studies is the Lyapunov function for a system linearized on a formal solution.

Keywords: ordinary differential equations, asymptotic solution, singular point, exact solution, Lyapunov function, dynamical system.

Funding Agency Grant Number
Russian Science Foundation 14-11-00078


DOI: https://doi.org/10.4213/mzm10667

Full text: PDF file (544 kB)
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English version:
Mathematical Notes, 2015, 98:5, 752–764

Bibliographic databases:

UDC: 517.928+531
Received: 26.02.2015

Citation: L. A. Kalyakin, “Lyapunov Functions in Justification Theorems for Asymptotics”, Mat. Zametki, 98:5 (2015), 695–709; Math. Notes, 98:5 (2015), 752–764

Citation in format AMSBIB
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