On one boundary-value problem for elliptic
differential-operator equations of the second order with quadratic spectral parameter
Authors
B. A. Aliev
Ин-т математики и механики HAH Азербайджана, Баку
N. K. Kurbanova
Ya. Yakubov
Abstract
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.
