Abstract
Березанский Леонид, д-р физ.-мат.наук, Департамент математики, Университет им. Бен- Гуриона в Негеве, г. Беэр-Шева, Израиль; brznsky@cs.bgu.ac.il. Leonid Berezansky, brznsky@cs.bgu.ac.il Ben-Gurion University of the Negev, Beer-Sheva, Israel
Highlights
In the present paper, a specially designed substitution transforms linear second order equations into a system, to which we apply some known exponential stability results
We proposed a substitution which exploits the parameters of the original model
For the nonlinear second order non-autonomous equations with delays we applied the linearization technique and the results obtained for linear models
Summary
For linear and nonlinear delay differential equations of the second order with damping terms exponential stability and global asymptotic stability conditions are obtained. The results are based on the new sufficient stability conditions for systems of linear equations. The results are illustrated with numerical examples, and a list of relevant problems for future research is presented. A broad class of the second order non-autonomous linear equations with delays was examined and explicit -verifiable sufficient stability conditions were obtained. For the nonlinear second order non-autonomous equations with delays we applied the linearization technique and the results obtained for linear models. Several numerical examples illustrate the application of the stability tests.
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