Geodesic
On the asymptotics of solutions of differential equations in Hilbert space
Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 485-501

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Solutions of differential equations of first and arbitrary order in Hilbert space are investigated; they arise in the study of elliptic problems in cylindrical domains and in domains with singular points. Existence theorems are obtained for a broad class of right sides, and the asymptotics of a solution as $t\to\infty$ is constructed under “minimal” conditions on the coefficients. The results make considerable progress possible in the study of qualitative properties of solutions of elliptic equations of higher order. 
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     author = {L. A. Bagirov and V. A. Kondrat'ev},
     title = {On the asymptotics of solutions of differential equations in {Hilbert} space},
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L. A. Bagirov; V. A. Kondrat'ev. On the asymptotics of solutions of differential equations in Hilbert space. Sbornik. Mathematics, Tome 72 (1992) no. 2, pp. 485-501. http://geodesic.mathdoc.fr/item/SM_1992_72_2_a12/