OSCILLATIONS OF SCALAR NEUTRAL IMPULSIVE DIFFERENTIAL EQUATIONS OF THE FIRST ORDER WITH VARIABLE COEFFICIENTS

The theory of oscillations of neutral impulsive differential equations is gradually occupying a central place among the theories of oscillations of impulsive differential equations. This could be due to the fact that neutral impulsive differential equations play fundamental roles in the present drive to further develop information technology. Indeed, neutral differential equations appear in networks containing lossless transmission lines (as in high-speed computers where the lossless transmission lines are used to interconnect switching circuits). In this paper, we generalize and prove the results of oscillations of neutral delay differential equations with constant coefficients obtained by Gyori and Ladas for impulsive differential equations.