On a one class of the solutions of the nonlinear first-order differential equation with oscillating coefficients
Journal Title: Дослідження в математиці і механіці - Year 2014, Vol 19, Issue 4
Abstract
For the nonlinear first-order differential equation, whose coefficients are represented as an absolutely and uniformly convergent Fourier-series with slowly varying coefficients and frequency, the condidtions of existence of the particular solution of analogous structure are obtained at resonance case.
Authors and Affiliations
S. A. Shchogolev
On the solution of the matrix Sylvester equation
Lyapunov matrix equations and their generalizations — Sylvester matrix equation widely used in the theory of stability of motion, as well as the solution of differential Riccati and Bernoulli equations. If the structure...
PRIME FACTORIZATION AND NORMAL NUMBERS
Research of the first author was supported in part by a grant from NSERC. Let 𝑞 > 2 be a fixed integer. Given an integer 𝑛 > 2 and writing its prime factorization as 𝑛 = 𝑝1𝑝2 ・ ・ ・ 𝑝𝑟 , where 𝑝1 6 𝑝2 6 ・ ・ ・ 6 𝑝𝑟 s...
ON THE STRUCTURE OF THE FUNDAMENTAL MATRIX OF THE LINEAR HOMOGENEOUS DIFFERENRIAL SYSTEM OF THE SPECIAL KIND
For the linear homogeneous differenrial system, whose coefficients are represented as an absolutely and uniformly convergent Fourier-series with slowly varying coefficients and frequency, the kind of the fundamental matr...
Variational method of homogeneous solutions for axisymmetric elasticity problems
A variational method of homogeneous solutions for solving of axisymmetric elasticity problems for semiinfinite and finite cylinders with free lateral surface has been developed. As an example of application of the method...
Approximation of periodical function in the weighted Orlicz spaces
We obtain some direct and inverse theorems of theory of approximation for 𝜓-differentiable functions in the metrics of weighted Orlicz spaces with weight functions, which belongs to the Muckenhoupt class.