Geodesic
On the asymptotic behavior of solutions of differential equations in Hilbert space
Izvestiya. Mathematics , Tome 6 (1972) no. 5, pp. 1067-1116

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Differential equations of arbitrary order with unbounded variable operator valued coefficients in a Hilbert space are considered. Asymptotic formulas for solutions are derived under the assumption that the coefficients are “weakly stabilized” at infinity. 
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     author = {V. G. Maz'ya and B. A. Plamenevskii},
     title = {On the asymptotic behavior of solutions of differential equations in {Hilbert} space},
     journal = {Izvestiya. Mathematics },
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V. G. Maz'ya; B. A. Plamenevskii. On the asymptotic behavior of solutions of differential equations in Hilbert space. Izvestiya. Mathematics , Tome 6 (1972) no. 5, pp. 1067-1116. http://geodesic.mathdoc.fr/item/IM2_1972_6_5_a6/