# Shchegolev S. A.

### 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.

### 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.

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

Kostin A. V., Shchegolev S. A.

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.

### 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.

### 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.

### 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.