The persistence of a general nonautonomous single-species Kolmogorov system with delays

In this paper, we establish some sufficient conditions for the persistence of system x′(t)=x(t)f(t,xt)x′(t)=x(t)f(t,xt) without the condition that f(t,φ)f(t,φ) is monotonously decreasing with respect to φφ. This partly answers the open problems proposed by Teng.