Asymptotic stability for a class of nonautonomous neutral differential equations (Q1377222)

Scalar nonlinear differential equations of the type \[ d/dt \bigl[x(t)-f(t,x(t-\tau))\bigr]+g(t,x(t-\delta))=0, \quad t \geq t_0, \] are considered. Here \(\tau ,\delta \in (0,\infty)\), \(g \in C([t_0, \infty)\times {\mathbb{R}},{\mathbb{R}})\) and \(xg(t,x) \geq 0\) for \(t \geq t_0 \), \(x \in {\mathbb{R}}\). Sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable are obtained.