Linear differential equations with unbounded delays and a forcing term

Jan Čermák and Petr Kundrát

Abstract and Applied Analysis, 2004, vol. 2004, 1-9

Abstract:

The paper discusses the asymptotic behaviour of all solutions of the differential equation y ˙ ( t ) = − a ( t ) y ( t ) + ∑ i = 1 n b i ( t ) y ( τ i ( t ) ) + f ( t ) , t ∈ I = [ t 0 , ∞ ) , 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.

Date: 2004
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlaaa:107032

DOI: 10.1155/S1085337504306020

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