Linear differential equations with unbounded delays and a forcing term
The paper discusses the asymptotic behaviour of all solutions of the differential equation y˙(t)=−a(t)y(t)+∑i=1nbi(t)y(τi(t))+f(t), t∈I=[t0,∞), with a positive continuous function a, continuous functions bi, f, and n continuously differentiable unbounded lags. We establish conditions under which any...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Hindawi Limited
2004-01-01
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| Series: | Abstract and Applied Analysis |
| Online Access: | http://dx.doi.org/10.1155/S1085337504306020 |
| Summary: | The paper discusses the asymptotic behaviour of all solutions of
the differential equation y˙(t)=−a(t)y(t)+∑i=1nbi(t)y(τi(t))+f(t), t∈I=[t0,∞),
with a positive continuous function a, continuous functions
bi, 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. |
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| ISSN: | 1085-3375 1687-0409 |