On one boundary-value problem for elliptic differential-operator equations of the second order with quadratic spectral parameter
AbstractThe 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.
How to Cite
AlievB. A., KurbanovaN. K., and YakubovY. “On One Boundary-Value Problem for elliptic differential-Operator Equations of the Second Order With Quadratic Spectral Parameter”. Ukrains’kyi Matematychnyi Zhurnal, Vol. 69, no. 6, June 2017, pp. 734-50, http://umj.imath.kiev.ua/index.php/umj/article/view/1732.