Stabilization of solutions of linear differential equations in Hilbert space

Conditions, less stringent than those known at present, are found for the stabilization of a solution of a linear differential equation of the form (du/dt) + A(t) u =f(t) in Hilbert space to a solution of the operational equation Ax =f, where A is a positive self-adjoint operator. Some regularization algorithms (in A. N. Tikhonov's sense) for this equation are investigated.Translated from Matematicheskie Zametki, Vol. 9, No. 4, pp. 415–420, April, 1971.I wish to thank Ya. I. Al'ber, O. A. Liskovts, and A. M. Il'in for their advice and useful comments.