On the asymptotics of solutions of differential equations in Hilbert space

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.