On exponential stability of second order delay differential equations

Agarwal, Ravi P. ; Domoshnitsky, Alexander ; Maghakyan, Abraham

Czechoslovak Mathematical Journal, Tome 65 (2015) no. 4, pp. 1047-1068

Abstract (VO)

We propose a new method for studying 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.

Détail

DOI : 10.1007/s10587-015-0227-9

Classification : 34K20
Keywords: delay equations; uniform exponential stability; exponential estimates of solutions; Cauchy function

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