The block diagonalization of the linear homogeneous differential system with coefficients of oscillating type in resonance case

Abstract

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 of existence of the linear transformation with coefficients of similar structure, this system leads to a block-diagonal form in a resonance case are obtained.

Authors and Affiliations

S. A. Shchogolev

Keywords

Related Articles

THE CRITERION FOR SOLVABILITY OF A LINEAR NOETHER’S BOUNDARY VALUE PROBLEM FOR A SYSTEM OF DYNAMICAL EQUATIONS ON A TIME SCALE

On a time scale, the linear Noether’s boundary value problem for a system of second-order dynamical equations is considered. This boundary-value problem is considered in the case when the operator of the linear part is i...

ASYMPTOTIC REPRESENTATIONS OF SOLUTIONS WITH SLOWLY VARYING DERIVATIVES

Second-order differential equations with power and exponential nonlinearities on the right hand side play an important role in the development of a qualitative theory of differential equations. The authors of most works...

Simultaneous approximation of locally integrable functions and their ψ-integrals

Low smoothness case. The article presents the problems of simultaneous approximation of locally integrable functions on the real axis of low smoothness and their integrals using Vallee Poussin operators. The asymptotic l...

ON THE MULTIPLICATIVE PARTITION FUNCTION

We study the number of representations n=s1⋯sm, where sj are sonor numbers, i.e. for every sj there do not exist the natural numbers n and k such that sj=nk, k⩾2. The counting function f(n) of such representation is the...

DYNAMICS OF A STOCHASTIC LOTKA–VOLTERRA FOOD CHAIN MODEL

The authors would like to thank Nguyen Hai Dang for his comments on the manuscript of this paper. This paper is concerned with a stochastic Lotka-Volterra food chain model. The existence of the global solution and the ul...

Download PDF file
  • EP ID EP191230
  • DOI -
  • Views 61
  • Downloads 0

How To Cite

S. A. Shchogolev (2016). The block diagonalization of the linear homogeneous differential system with coefficients of oscillating type in resonance case. Дослідження в математиці і механіці, 21(2), 63-75. https://europub.co.uk./articles/-A-191230