On the asymptotic proximity of the solutions of a Cauchy problem for first-order differential equations in a Banach space (Q1390443)

The author deals with an equation of the form \[ v'(t)= \sum^n_{i= 1}a_i(t) A_iv(t),\tag{1} \] where \(A_i\), \(i= 1,2,\dots, n\), are commuting generators of strongly continuous cosine-functions defined on a (B)-space and \(a_i: [0,+\infty)\to [0,+\infty)\) are continuous and bounded functions. The author provides conditions for the proximity as \(t\to+\infty\) of solutions to (1) with solutions to the equation \(w'(t)= \sum^n_{i= 1}a_i A_iw(t)\), where \(a_i\) are appropriate constants.