Geodesic
On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients
Izvestiya. Mathematics , Tome 7 (1973) no. 6, pp. 1327-1370.

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A system of differential equations on the semiaxis $T$ 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. 
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B. A. Plamenevskii. On the asymptotic behavior of solutions of quasielliptic differential equations with operator coefficients. Izvestiya. Mathematics , Tome 7 (1973) no. 6, pp. 1327-1370. http://geodesic.mathdoc.fr/item/IM2_1973_7_6_a6/

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