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.

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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