On the oscillations in the quasi-linear second order differential systems with slowly-varying parameters

Abstract

For the quasi-linear second order differential system with pure imaginary eigenvalues of the matrix of the linear part, the conditions of the existence of the particular solution, representable as an absolutely and uniformly convergent Fourier-series with slowly varying coefficients and frequency, are obtained at the asymptotic long interval of the independent variable.

Authors and Affiliations

S. A. Shchogolev

Keywords

Related Articles

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...

On a two-step algorithm in structural and parametric optimization problems of linear control systems.

This paper deals with applying of a two-step optimization algorithm for structural and parametric optimization problems of linear control systems with fixed and floating switching points.

On the one self-improving property of exponent

In this note an alternative proof of the well-known property, associated with the so-called “self-improving property”, is presented. This property states that if for some 𝐵 > 1, 1 < 𝑞 < ∞, nonnegative on (0,+∞) function...

Axisymmetric torsion problem for the finite length multilayered cylinder

The exact solution of the axysimmetric elasticity problem on the torsion of the multilayered massive and hollow cylinder under an influence of the torsion loading at the lateral cylinder’ surface. The layers are in the c...

About additive operation on set of discrete random variable

Authors propose an approach to determine an additive operation on set of discrete random variables. Result of this operation has as much possible values, how many operands. Conditions under which operation is commutative...

Download PDF file
  • EP ID EP416106
  • DOI -
  • Views 45
  • Downloads 0

How To Cite

S. A. Shchogolev (2014). On the oscillations in the quasi-linear second order differential systems with slowly-varying parameters. Дослідження в математиці і механіці, 19(2), 75-86. https://europub.co.uk/articles/-A-416106