On exponential stability of second order delay differential equations. (English) Zbl 1363.34250

Summary: We propose a new method for studying the stability of second-order delay differential equations. Results we obtained are of the form: the exponential stability of ordinary differential equation implies the exponential stability of the corresponding delay differential equation if the delays are small enough. We estimate this smallness through the coefficients of this delay equation. Examples demonstrate that our tests of the exponential stability are essentially better than the known ones. This method works not only for autonomous equations but also for equations with variable coefficients and delays.


34K20 Stability theory of functional-differential equations
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