A new stability test for linear neutral differential equations

We obtain new explicit exponential stability conditions for the linear scalar neutral equation with two bounded delays $\dot{x}(t)-a(t)\dot{x}(g(t))+b(t)x(h(t))=0,$ where $0\leq a(t)\leq A_0<1$, $0<b_0\leq b(t)\leq B$, 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.