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Preservation of exponential stability for equations with several delays

We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays x˙ (t) + ∑m k=1 ak(t)x(hk(t)) = 0, ak(t) ≥ 0 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.