Linear differential equations with unbounded delays and a forcing term (Q1773515)

Summary: The paper discusses the asymptotic behaviour of all solutions of the differential equation \[ \dot y(t)= -a(t)y(t)+ \sum^n_{i=1} b_i(t) y(\tau_i(t))+ f(t),\;t\in I= [t_0,\infty), \] with a positive continuous function \(a\), continuous functions \(b_i\), \(f\), and \(n\) continuously differentiable unbounded lags. We establish conditions under which any solution y of this equation can be estimated by means of a solution of an auxiliary functional equation with one unbounded lag. Moreover, some related questions concerning functional equations are discussed as well.