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

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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.

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Authors and Affiliations

  1. Voronezh State University, Voronezh, Russia

    A. I. Perov & I. D. Kostrub

Authors
  1. A. I. Perov
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  2. I. D. Kostrub
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Correspondence to A. I. Perov.

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Original Russian Text Copyright © 2016 Perov A.I. and Kostrub I.D.

Voronezh. Translated from Sibirskiĭ Matematicheskiĭ Zhurnal, Vol. 57, No. 4, pp. 830–849, July–August, 2016; DOI: 10.17377/smzh.2016.57.408. Original article submitted September 22, 2015.

The authors were supported by the Russian Foundation for Basic Research (Grant 16–01–00197).

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Perov, A.I., Kostrub, I.D. On bounded solutions to weakly nonlinear vector-matrix differential equations of order n . Sib Math J 57, 650–665 (2016). https://doi.org/10.1134/S003744661604008X

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  • DOI: https://doi.org/10.1134/S003744661604008X

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