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 $\frac{du}{dt}+A(t)u=f(t)$ 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.