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On exponential stability of a linear delay differential equation with an oscillating coefficient. (English) Zbl 1187.34096

Summary: New explicit exponential stability conditions are obtained for the nonautonomous linear equation

x ˙(t)=a(t)x(h(t))=0,

where h(t)t and a(t) is an oscillating function.

We apply the comparison method based on the Bohl-Perron type theorem. Coefficients and delays are not assumed to be continuous.

Some real-world applications and several examples are also discussed.

MSC:
34K20Stability theory of functional-differential equations
34K06Linear functional-differential equations
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