2019
Том 71
№ 11

All Issues

Aliev B. A.

Articles: 3
Article (Russian)

On one boundary-value problem for elliptic differential-operator equations of the second order with quadratic spectral parameter

Aliev B. A., Kurbanova N. K., Yakubov Ya.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2017. - 69, № 6. - pp. 734-750

The problem of solvability of a boundary-value problem for a differential-operator equation of the second order on a finite interval is studied in a complex separable Hilbert space H in the case where the same spectral parameter appears in the equation in the form of a quadratic function and in the boundary conditions in the form of a linear function and, moreover, the boundary conditions are not separated. The asymptotic behavior of the eigenvalues of one homogeneous abstract boundary-value problem is also investigated. The asymptotic formulas for the eigenvalues are obtained and an application of the obtained results to partial differential equations is analyzed.

Article (Russian)

Solvability of the boundary-value problem for the second-order elliptic differential-operator equation with spectral parameter in the equation and boundary conditions

Aliev B. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2010. - 62, № 1. - pp. 3 - 14

We investigate the solvability of a boundary-value problem for second-order elliptic operator differential equation with a spectral parameter in the equation and boundary conditions. We also study the asymptotic behavior of eigenvalues corresponding to a homogeneous boundary-value problem.

Brief Communications (Russian)

Asymptotic behavior of the eigenvalues of a boundary-value problem for a second-order elliptic operator-differential equation

Aliev B. A.

↓ Abstract   |   Full text (.pdf)

Ukr. Mat. Zh. - 2006. - 58, № 8. - pp. 1146–1152

We study the asymptotic behavior of the eigenvalues of a boundary-value problem with spectral parameter in the boundary conditions for a second-order elliptic operator-differential equation. The asymptotic formulas for the eigenvalues are obtained.