We consider the second order initial value problem in a Hilbert space, which is a singular perturbation of a first order initial value problem. The difference of the solution and its singular limit is estimated in terms of the small parameter $\varepsilon .$ The coefficients are commuting self-adjoint operators and the estimates hold also for the semilinear problem.
 Fattorini, H.O.: Second Order Linear Differential Equations in Banach Spaces
. North Holland, 1985. MR 0797071
| Zbl 0564.34063