2019
Том 71
№ 2

All Issues

Apakov Yu. P.

Articles: 4
Brief Communications (Russian)

Third boundary-value problem for a third-order differential equation with multiple characteristics

Apakov Yu. P.

↓ Abstract

Ukr. Mat. Zh. - 2018. - 70, № 9. - pp. 1274-1281

We prove the unique solvability of the third boundary-value problem for a third-order differential equation with multiple characteristics containing the second time derivative in a rectangular domain.

Article (Russian)

Boundary-Value Problem for a Degenerate High-Odd-Order Equation

Apakov Yu. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2014. - 66, № 10. - pp. 1318–1331

We consider a boundary-value problem for a degenerate high-odd-order equation. The uniqueness of the solution is shown by the method of energy integrals. The solution is constructed by the method of separation of variables. In this case, we get the eigenvalue problem for a degenerate even-order ordinary differential equation. The existence of eigenvalues is proved by means of reduction to the integral equation.

Article (Russian)

On the solution of a boundary-value problem for a third-order equation with multiple characteristics

Apakov Yu. P.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2012. - 64, № 1. - pp. 3-13

We consider the first boundary-value problem for the third-order equation with multiple characteristics $u_{x x x} - u_{y y} = f (x,y)$ in the domain $D = \{ ( x , y ) : 0 < x < p, 0 < y < l\}$ The uniqueness of a solution is proved by the energy-integral method, and the solution is constructed in explicit form with the use of the Green function.

Article (Russian)

On the theory of the third-order equation with multiple characteristics containing the second time derivative

Apakov Yu. P., Dzhuraev T. D.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 1. - pp. 40 - 51

We construct a fundamental solution of the third-order equation with multiple characteristics containing the second time derivative, establish the estimates valid for large values of the argument, and study some properties of fundamental solutions necessary for the solution of boundary-value problems.