On bounded solutions to weakly nonlinear vector-matrix differential equations of order n
- Authors: Perov A.I.1, Kostrub I.D.1
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Affiliations:
- Voronezh State University
- Issue: Vol 57, No 4 (2016)
- Pages: 650-665
- Section: Article
- URL: https://journals.rcsi.science/0037-4466/article/view/170603
- DOI: https://doi.org/10.1134/S003744661604008X
- ID: 170603
Cite item
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.
About the authors
A. I. Perov
Voronezh State University
Author for correspondence.
Email: anperov@mail.ru
Russian Federation, Voronezh
I. D. Kostrub
Voronezh State University
Email: anperov@mail.ru
Russian Federation, Voronezh
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