Global stability for separable nonlinear delay differential equations,

Consider the following separable nonlinear delay differential equation , where we assume that, there is a strictly monotone increasing function f(x) on (−∞, +∞) such that In this paper, to the above separable nonlinear delay differential equation, we establish conditions of global asymptotic stability for the zero solution. In particular, for a special wide class of f(x) which contains a case of f(x) = ex−1, we give more explicit conditions. Applying these, we offer conditions of global asymptotic stability for solutions of nonautonomous logistic equations with delays.