Leonid Berezansky, Department of Mathematics, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel, e-mail: brznsky@cs.bgu.ac.il; Elena Braverman, Department of Mathematics and Statistics, University of Calgary, 2500 University Drive N.W., Calgary, AB T2N 1N4, Canada, e-mail: maelena@math.ucalgary.ca (corresponding author)
Abstract: We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays
\dot{x}(t) + \sum_{k=1}^m a_k(t) x(h_k(t)) = 0, \quad a_k(t) \geq0
under the addition of new terms and a delay perturbation. We assume that the original equation has a positive fundamental function; our method is based on Bohl-Perron type theorems. Explicit stability conditions are obtained.
Keywords: exponential stability, nonoscillation, explicit stability condition, perturbation
Classification (MSC 2010): 34K20
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