Oscillation and nonoscillation for systems of two first-order linear differential equations with delay

Abstract

Functional differential equations with delay provide a mathematical model for a physical or biology system in which the rate of change of the system depends upon its past history. In the literature, there are several papers [14] concerning the study of oscillatory behavior of solutions of first order differential equations with time delay. But there are few results [S] about the oscillation of linear system of first order equation with delay. In this paper, we study the oscillatory behavior of linear system with delay. First, in Section 2, we consider the case of constant coefficients in details. We show that the delay can cause or destroy the oscillations. We present constructive procedure to generate or destroy oscillations of a system. In section 3 we consider the case of variable coefficients and obtain some results analogous to the result in Section 2.