2019
Том 71
№ 6

All Issues

Sokil B. I.

Articles: 9
Article (Ukrainian)

On the application of Ateb-functions to the construction of an asymptotic solution of the perturbed nonlinear Klein-Gordon equation

Mitropolskiy Yu. A., Sokil B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1998. - 50, № 5. - pp. 665–670

For the perturbed nonlinear Klein-Gordon equation, we construct an asymptotic solution by using Ateb-functions. We consider autonomous and nonautonomous cases.

Brief Communications (Ukrainian)

On asymptotic approximation of a solution of a boundary-value problem for a nonlinear nonautonomous equation

Sokil B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 11. - pp. 1580–1583

On the basis of periodic Ateb functions, in the resonance and nonresonance cases, we construct the asymptotic approximation of one-frequency solutions of a boundary-value problem for a nonlinear nonautonomous equation.

Brief Communications (Ukrainian)

On the application of Ateb-functions to the construction of a solution of a nonlinear Klein-Gordon equation

Sokil B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1997. - 49, № 6. - pp. 872–877

For a nonlinear Klein-Gordon equation, we construct the first approximation of an asymptotic solution by using Ateb-functions. The resonance and nonresonance cases are considered.

Brief Communications (Russian)

Application of ateb-functions to the construction of solutions of some nonlinear partial differential equations

Sokil B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1996. - 48, № 2. - pp. 287-288

We construct asymptotic approximations of one-frequency solutions of some nonlinear partial differential equations by using periodic Ateb-functions.

Article (Ukrainian)

Construction of one-frequency solutions of boundary-value problems for a nonautonomous wave equation

Sokil B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 9. - pp. 1275–1279

By using special periodic Ateb-functions, we construct asymptotic representations of one-frequency solutions of boundary-value problems for a nonautonomous wave equation.

Article (Ukrainian)

On a method for constructing one-frequency solutions of a nonlinear wave equation

Sokil B. I.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 1994. - 46, № 6. - pp. 782–784

A method for constructing one-frequency solutions of nonlinear wave equations is suggested. This approach is based on a modified representation of asymptotic expansions by using special periodic Atebfunctions. This method makes it possible to obtain approximate solution of the problem under consideration without difficulty.

Article (Ukrainian)

Asymptotic representation of the solution of a nonlinear system with resonance

Sokil B. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1983. - 35, № 3. - pp. 390 — 392

Article (Ukrainian)

Asymptotic expansions of a boundary-value problem for a certain nonlinear partial differential equation

Sokil B. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1982. - 34, № 6. - pp. 803—805

Article (Ukrainian)

An asymptotic expansion for a class of nonlinear differential equations

Barvinskii A. F., Sokil B. I.

Full text (.pdf)

Ukr. Mat. Zh. - 1980. - 32, № 5. - pp. 686–693