Geodesic
Preservation of exponential stability for equations with several delays
Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 135-144

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We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $$ \dot {x}(t) + \sum _{k=1}^m a_k(t) x(h_k(t)) = 0, \quad a_k(t) \geq 0 $$ 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.
We consider preservation of exponential stability for the scalar nonoscillatory linear equation with several delays $$ \dot {x}(t) + \sum _{k=1}^m a_k(t) x(h_k(t)) = 0, \quad a_k(t) \geq 0 $$ 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.
DOI : 10.21136/MB.2011.141576
Classification : 34K06, 34K20, 34K27, 47N20
Keywords: exponential stability; nonoscillation; explicit stability condition; perturbation 
Berezansky, Leonid; Braverman, Elena. Preservation of exponential stability for equations with several delays. Mathematica Bohemica, Tome 136 (2011) no. 2, pp. 135-144. doi: 10.21136/MB.2011.141576
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