ON THE ASYMPTOTIC BEHAVIOR OF SOLUTIONS OF QUASIELLIPTIC DIFFERENTIAL EQUATIONS WITH OPERATOR COEFFICIENTS
Boris Alekseevich Plamenevskii · Mathematics of the USSR-Izvestiya · 1973
A system of differential equations on the semiaxis is considered with operator coefficients in a Hilbert space. The coefficients of the system depend on and for are stabilized in a certain sense. The spectrum of the limit operator consists of normal eigenvalues and is contained inside a certain double angle with opening less than which contains the imaginary axis. Asymptotic formulas are derived for the solution, and the contribution which a multiple eigenvalue of the limiting operator pencil makes to the asymptotic expressions is investigated. Bibliography: 17 titles.