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Sibirskii Matematicheskii Zhurnal, 2016, Volume 57, Number 4, Pages 830–849
DOI: https://doi.org/10.17377/smzh.2016.57.408 (Mi smj2787) 		 
This article is cited in 6 scientific papers (total in 6 papers)

On bounded solutions to weakly nonlinear vector-matrix differential equations of order $n$

A. I. Perova, I. D. Kostrub

a Voronezh State University, Voronezh, Russia
Full-text PDF (348 kB) Citations (6)
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DOI: https://doi.org/10.17377/smzh.2016.57.408
Abstract: To prove existence and uniqueness (or just existence) of a bounded solution to nonlinear differential equations of higher order, we employ the contraction mapping principle and the Tikhonov Fixed Point Theorem. A quantitative estimate of a nonlinear perturbation preserving basic features of behavior of the corresponding linear equation (asymptotic stability or exponential dichotomy) is important when we pass to a nonlinear equation.
Keywords: nonlinear systems of differential equations, bounded solution, contraction mapping principle, Tikhonov Fixed Point Theorem.
Funding agency Grant number
Russian Foundation for Basic Research 16-01-00197
The authors were supported by the Russian Foundation for Basic Research (Grant 16-01-00197).
Received: 22.09.2015
English version:
Siberian Mathematical Journal, 2016, Volume 57, Issue 4, Pages 650–665
DOI: https://doi.org/10.1134/S003744661604008X
Bibliographic databases:
Document Type: Article
UDC: 517.925.54
Language: Russian
Citation: A. I. Perov, I. D. Kostrub, “On bounded solutions to weakly nonlinear vector-matrix differential equations of order $n$”, Sibirsk. Mat. Zh., 57:4 (2016), 830–849; Siberian Math. J., 57:4 (2016), 650–665
Citation in format AMSBIB
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    • This publication is cited in the following 6 articles:
    Citing articles in Google Scholar: Russian citations, English citations
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