Geodesic
Stability of delay differential equations with oscillating coefficients
Electronic Journal of Differential Equations, Tome 2010 (2010).

Voir la notice de l'article provenant de la source Electronic Library of Mathematics

Summary: 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__a233,
     author = {Gil', Michael I.},
     title = {Stability of delay differential equations with oscillating coefficients},
     journal = {Electronic Journal of Differential Equations},
     publisher = {mathdoc},
     volume = {2010},
     year = {2010},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/EJDE_2010__2010__a233/}
}
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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__a233/