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We are concerned with a class of n-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of delay differential equations. Sufficient conditions for the exponential asymptotic stability of the linear system are established. By using this stability, the permanence of the perturbed nonlinear system is studied. Under more restrictive constraints on the coefficients, the system has a cooperative type behaviour, in which case explicit uniform lower and upper bounds for the solutions are obtained. As an illustration, the asymptotic behaviour of a non-autonomous Nicholson system with distributed delays is analysed. [ABSTRACT FROM AUTHOR]

We consider a characteristic equation to analyze asymptotic stability of a scalar renewal equation, motivated by structured population dynamics models. The characteristic equation is given by 1 = ∨ 0∞ k(a)e-Μ ada, where k : R+ R can be decomposed into positive and negative parts. It is shown that if delayed negative feedback is characterized by a convex function, then all roots of the characteristic equation locate in the left half complex plane. [ABSTRACT FROM AUTHOR]

In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and generalize the main results of the key references in this subject. An illustrative example is also provided. [ABSTRACT FROM AUTHOR]