Oscillation of delay diffrential equations with a middle term

Abstract

This thesis is concerned with the oscillation of delay differential equations with a middle term. This type of equation appears in several applications in physical and engineering systems. The existence of middle term adds extra difficulties to the study of oscillation theory for delay differential equations. Indeed, the middle term can change the qualitative behavior of solutions. Recently, considerable attention have been devoted to study the oscillation of delay differential equations with a middle term. In this thesis we present several theorems for the oscillation of third and fourth order delay differential equations with a middle term. Linear and nonlinear equations are considered, as well as several examples are given. In general, the oscillation results of such equations are deduced by using two approaches. The first is applying a suitable Riccati type transformation to reduce the studied equation to a first order Riccati inequality. The second is applying suitable comparison principles.