ASYMPTOTIC STABILITY FOR A CLASS OF NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATIONS

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ASYMPTOTIC STABILITY FOR A CLASS OF NONAUTONOMOUS NEUTRAL DIFFERENTIAL EQUATIONS

Consider the scalar nonlinear delay differential equation $$\frac{d}{dt}x(t)-f(t,x(t-\tau))] + g(t,x(t-\delta)) = 0,\ \ t\ge t_0,$$ where $\tau,\delta\in(0,\infty), f,g \in C(t_0,\infty)\times \R,\R)$ and $xg(t,x)\ge 0$ for $t\ge t_0, x\in \R.$ The author obtains sufficient conditions for the zero solution of this equation to be uniformly stable as well as asymptotically stable.