TY - JOUR
AU - B. A. Aliev
AU - N. K. Kurbanova
AU - Ya. Yakubov
PY - 2017/06/25
Y2 - 2020/12/03
TI - On one boundary-value problem for elliptic
differential-operator equations of the second order with quadratic spectral parameter
JF - Ukrainsâ€™kyi Matematychnyi Zhurnal
JA - Ukr. Mat. Zhurn.
VL - 69
IS - 6
SE - Research articles
DO -
UR - http://umj.imath.kiev.ua/index.php/umj/article/view/1732
AB - The problem of solvability of a boundary-value problem for a differential-operator equation of the second order on afinite interval is studied in a complex separable Hilbert space H in the case where the same spectral parameter appearsin 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 homogeneousabstract boundary-value problem is also investigated. The asymptotic formulas for the eigenvalues are obtained and anapplication of the obtained results to partial differential equations is analyzed.
ER -