On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients

A system of differential equations on the semiaxis $T<t<+\infty$ is considered with operator coefficients in a Hilbert space. The coefficients of the system depend on $t$ and for $t\to+\infty$ 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 $\pi$ 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.