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 75
- Downloads 0
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 THE EXISTENCE OF AN INTEGRAL MANIFOLD OF A SPECIAL TYPE OF A SOME NONLINEAR DIFFERENTIAL SYSTEM
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 fu...
Noninvertible analogue for the congugate mapping for the pair of tent-like mappings
The functional equation which appear in the definition of the topological conjugacy of the tent-like piecewise linear mappings of an interval into itself. All the solutions of this functional equations are obtained and t...
HIGH-ORDER CLUSTER INTEGRALS FOR THE LATTICE-GAS MODEL
In the paper, for the known statistical lattice-gas model, a new method is proposed to define the high-order reducible cluster integrals on the basis of the Cauchy--Hadamard theorem and recently established strict inform...
Initial-boundary value problems for nonlinear parabolic equations with the variable exponents of nonlinearity and integral operators type Volterra
Initial-boundary value problems for nonlinear Volterra integro-differential equations with the variable exponents of nonlinearity are investigated. Weak solutions which belong to the generalized Sobolev and Lebesgue spac...