ON THE EXISTENCE OF AN INTEGRAL MANIFOLD OF A SPECIAL TYPE OF A SOME NONLINEAR DIFFERENTIAL SYSTEM
Journal Title: Дослідження в математиці і механіці - Year 2015, Vol 20, Issue 2
Abstract
A nonlinear system of the differential equations is considered. This system is a linear extension of the nonlinear differential equation on a circle. The coefficients of the system belong to the class F, which are the functions that can be represented in the form of the absolutely and uniformly convergent Fourier series on the entire axis with slowly varying coefficients in a certain sense and frequencies. The basic properties of this functions’ class are investigated. This system is expected as a close one to an inhomogeneous linear system of the differential equations with a diagonal matrix of the slowly varying coefficients and free terms, belonging to the class F. The transformations with the coefficients of class F, causing the system to a system in which the frequency is determined from the nonlinear equations with slowly varying coefficients, are constructed using the contraction mapping principle. As a result, the conditions, under which the original system has an integral manifold of class F, are considered.
Authors and Affiliations
S. A. Shchogolev
Keywords
Related Articles
- EP ID EP417178
- DOI -
- Views 84
- Downloads 0
Step average linear differential inclusions of variable dimension
The theory of differential inclusions began its development in the early thirties of the 20th century with the publication A. Marsh and S. Zaremba. However, the rapid development of this theory began with the 60s of the...
Asymptotic of rapid varying solutions of differential equations of the second order with rapid varying nonlinearities
The question of the asymptotic behavior of the differential equations’ solution by 𝑡 ↑ 𝜔 𝑦′′ = 𝛼0𝑝(𝑡)𝜙(𝑦), where 𝛼0 ∈ {−1, 1}, 𝑝 : [𝑎, 𝜔[−→]0,+∞[ is a continuous function, −∞ < 𝑎 < 𝜔 6 +∞ , 𝜙 : Δ𝑦0 −→]0,+∞[ is a twice co...
About the characteristic polynomial of product Frobenius’ matrix
The formula for calculating characteristic polynomials of product Frobenius’ matrix was obtained. The opportunity of using this formula by the tasks of control of nonlinear discret systems was shown.
QA-DEFORMATION OF SURFACE OF NEGATIVE GAUSSIAN CURVATURE
An infinitesimal deformation with the given law of changing the element of area of a surface in Euclidean three-space was considered in this article. Such deformation in the article was called the quasiareal infinitesima...
The block diagonalization of the linear homogeneous differential system with coefficients of oscillating type in resonance case
For the linear homogeneous system of the differential equations, coefficients of which are represented by an absolutely and uniformly convergent Fourier series with slowly varying coefficients and frequency, conditions o...