A new stability test for linear neutral differential equations

Abstract We obtain new explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays x ( t ) − a ( t ) x ( g ( t ) ) + b ( t ) x ( h ( t ) ) = 0 , where 0 ≤ a ( t ) ≤ A 0 1 , 0 b 0 ≤ b ( t ) ≤ B , using the Bohl–Perron theorem and a transformation of the neutral equation into a differential equation with an infinite number of delays. The results are applied to the neutral logistic equation.

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