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Matematicheskie Zametki, 2015, Volume 98, Issue 5, Pages 695–709
DOI: https://doi.org/10.4213/mzm10667 (Mi mzm10667) 		 
This article is cited in 8 scientific papers (total in 8 papers)

Lyapunov Functions in Justification Theorems for Asymptotics

L. A. Kalyakin

Institution of Russian Academy of Sciences Institute of Mathematics with Computer Center, Ufa
Full-text PDF (544 kB) Citations (8)
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DOI: https://doi.org/10.4213/mzm10667
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
Received: 26.02.2015
English version:
Mathematical Notes, 2015, Volume 98, Issue 5, Pages 752–764
DOI: https://doi.org/10.1134/S000143461511005X
Bibliographic databases:
Document Type: Article
UDC: 517.928+531
Language: Russian
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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    • This publication is cited in the following 8 articles:
    1. Oskar A. Sultanov, “Asymptotic regimes in oscillatory systems with damped non-resonant perturbations”, Nonlinear Dyn, 112:4 (2024), 2589  crossref
    2. Oskar A. Sultanov, “Resonance in Isochronous Systems with Decaying Oscillatory Perturbations”, Qual. Theory Dyn. Syst., 23:S1 (2024)  crossref
    3. Oskar A. Sultanov, “Nonlinear resonance in oscillatory systems with decaying perturbations”, DCDS, 2024  crossref
    4. L. A. Kalyakin, “Asymptotics of the Solution of a Variational Problem on a Large Interval”, Math. Notes, 110:5 (2021), 687–699  mathnet  crossref  crossref  isi  elib
    5. Kiselev O.M., “An Asymptotic Structure of the Bifurcation Boundary of the Perturb E D Painleve-2 Equation”, Chaos Solitons Fractals, 151 (2021), 111299  crossref  mathscinet  isi
    6. O. A. Sultanov, “Lyapunov Functions and Asymptotics at Infinity of Solutions of Equations that are Close to Hamiltonian Equations”, J Math Sci, 258:1 (2021), 97  crossref
    7. O. A. Sultanov, “Funktsii Lyapunova i asimptotika na beskonechnosti reshenii uravnenii, blizkikh k gamiltonovym”, Differentsialnye uravneniya, Itogi nauki i tekhn. Sovrem. mat. i ee pril. Temat. obz., 163, VINITI RAN, M., 2019, 96–107  mathnet  mathscinet
    8. O. Sultanov, “Lyapunov functions and asymptotic analysis of a complex analogue of the second Painleve equation”, Vii International Conference Problems of Mathematical Physics and Mathematical Modelling, Journal of Physics Conference Series, 1205, IOP Publishing Ltd, 2019, 012056  crossref  isi
    Citing articles in Google Scholar: Russian citations, English citations
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