On one boundary-value problem for elliptic differential-operator equations of the second order with quadratic spectral parameter
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.
Citation Example: Aliev B. A., Kurbanova N. K., Yakubov Ya. 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.