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Linear differential equations with unbounded delays and a forcing term. (English) Zbl 1104.34053

Siafarikas, Panayiotis D. (ed.), International conference on differential, difference equations and their applications, July 1–5, 2002, Patras, Greece. Cairo: Hindawi Publishing Corporation (ISBN 977-5945-14-3/hbk). 83-91 (2004).
Summary: The paper discusses the asymptotic behaviour of all solutions of the differential equation \[ \dot y(t)=-a(t)y(t)+\sum^n_{i=1}b_i(t)y\bigl( \tau_i(t) \bigr)+f(t),\;t\in I=[t_0,\infty), \] 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.
For the entire collection see [Zbl 1089.34002].

MSC:

34K25 Asymptotic theory of functional-differential equations
34K06 Linear functional-differential equations
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