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Linear differential equations with unbounded delays and a forcing term. (English) Zbl 1066.34078

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.

MSC:

34K25 Asymptotic theory of functional-differential equations
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