Geodesic
Stability of delay differential equations with oscillating coefficients
Electronic journal of differential equations, Tome 2010 (2010)
We study the solutions to the delay differential equation equation

$ \dot x(t)=-a(t)x(t-h), $

where the coefficient $a(t)$ is not necessarily positive. It is proved that this equation is exponentially stable provided that $a(t)=b+c(t)$ for some positive constant b less than $\pi/(2h)$, and the integral $\int_0^t c(s)ds$ is sufficiently small for all $t>0$. In this case the 3/2-stability theorem is improved.
Classification : 34K20
Keywords: linear delay differential equation, exponential stability 
@article{EJDE_2010__2010__a33,
     author = {Gil',  Michael I.},
     title = {Stability of delay differential equations with oscillating coefficients},
     journal = {Electronic journal of differential equations},
     year = {2010},
     volume = {2010},
     zbl = {1200.34083},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a33/}
}
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%J Electronic journal of differential equations
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%U http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a33/
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Gil',  Michael I. Stability of delay differential equations with oscillating coefficients. Electronic journal of differential equations, Tome 2010 (2010). http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a33/