Aliev B. A.
On one boundary-value problem for elliptic differential-operator equations of the second order with quadratic spectral parameter
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.
Solvability of the boundary-value problem for the second-order elliptic differential-operator equation with spectral parameter in the equation and boundary conditions
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.
Asymptotic behavior of the eigenvalues of a boundary-value problem for a second-order elliptic operator-differential equation
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.