2019
Том 71
№ 11

# Shchegolev S. A.

Articles: 6
Brief Communications (Russian)

### A resonance case of the existence of solutions of a quasilinear second-order differential system, which are represented by Fourier series with slowly varying parameters

Ukr. Mat. Zh. - 1999. - 51, № 2. - pp. 285–288

For a quasilinear second-order differential system, whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove, under certain conditions, the existence of a particular solution having a similar structure. This result is obtained in the case where the characteristic equation possesses purely imaginary roots, which satisfy a certain resonance relation.

Article (Ukrainian)

### On one class of solutions of a countable quasilinear system of differential equations with slowly varying parameters

Ukr. Mat. Zh. - 1998. - 50, № 8. - pp. 1121–1128

For a countable quasilinear differential system whose coefficients are represented as Fourier series with slowly varying coefficients and frequency, we present conditions under which solutions of this system have analogous structure.

Article (Russian)

### On solutions of a second-order quasilinear differential system representable by Fourier series with slowly varying parameters

Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 654–664

For a second-order quasilinear differential system whose coefficients have the form of Fourier series with slowly varying coefficients and frequency, we prove that, under certain conditions, there exists a particular solution with a similar structure in the case of purely imaginary roots of the characteristic equation for the matrix of coefficients of the linear part.

Article (Russian)

### Construction of a solution of a quasilinear partial differential equation of parabolic type with oscillating and slowly varying coefficients

Ukr. Mat. Zh. - 1995. - 47, № 8. - pp. 1129–1135

We study a boundary-value problem for a partial differential equation of parabolic type with coefficients in the form of Fourier series with coefficients and frequency slowly varying in time.

Article (Russian)

### On solutions of a quasilinear almost triangular system of difference equations

Ukr. Mat. Zh. - 1995. - 47, № 4. - pp. 525–530

For an almost triangular system of difference equations, the problem of existence of particular solutions in the form of Fourier series with slowly varying coefficients and frequency is studied.

Article (Russian)

### On the solution of a quasilinear differential system with periodic coefficients

Ukr. Mat. Zh. - 1993. - 45, № 8. - pp. 1157–1161

The existence of a partial solution is proved for a quasilinear differential system whose coefficients are representable by a trigonometric series with slowly varying coefficients and frequency. The solution obtained has the same structure.