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Negativity of delayed induced oscillations in a simple linear DDE. (English) Zbl 1218.34079
Oscillatory behaviour appearing in the equation
$\frac{dx}{dt} = A-Bx(t)-Cx(t-\tau)$
with $$B < C$$ and $$\tau \geq (c^2-B^2)^{-1/2}\cos^{-1}(-B/C)$$ is studied. It is shown that, for a solution with $$x(s)=0$$ for $$s<0$$ and $$x(0)=x^0\geq 0$$, and some other initial values, there exists always a $$t\in (0, 4\tau)$$ such that $$x(t)<0$$. This shows that the proposed Cauchy problem is not a proper description of biochemical reactions or of other biological and physical quantities.

MSC:
 34K11 Oscillation theory of functional-differential equations 34K06 Linear functional-differential equations
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