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Solution estimates for linear differential equations with delay
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DOI：10.1016/j.amc.2019.124962.png)
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Abstract
En 中文
In this paper, we give explicit exponential estimates vertical bar x(t)vertical bar <= Me-gamma(t-t0), where t >= t(0), M> 0, for solutions of a linear scalar delay differential equation (x) over dot + Sigma(m )(k=1)b(k)(t)x(h(k)(t)) = f(t), t >= t(0), x(t) = phi(t), t <= t(0). We consider two different cases: when gamma > 0 (corresponding to exponential stability) and the case of gamma < 0 when the solution is, generally, growing. In the first case, together with the exponential estimate, we also obtain an exponential stability test, in the second case we get estimation for solution growth. Here both the coefficients and the delays are measurable, not necessarily continuous. (C) 2019 Elsevier Inc. All rights reserved.
Keywords:
Linear delay differential equations
Explicit solution estimates
Variable delays and coefficients
Exponential stability
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