Faisal Al-dheleai

Oscillation of Certain Types of Second Order Differential Equations Faisal Al-dheleai

It is well known that the differential equations fined a wide range of application in biological, physical, social and engineering. The interest on second order differential equations is due, in large part,to the fact that many physical systems are modeled by second order ordinary differential equations. For example, the so -called Emden-Fowler equation arises in the study of gas dynamics and fluid mechanics. The equation appears also in the study of relativistic mechanics, nuclear physics and in the study of chemically reacting systems. So, finding the solutions of the differential equations or deducing important characteristics of it has received the attention of many authors. In this work,via Integral averaging technique and Interval technique, we presented sufficient conditions for the oscillatory of the second order nonlinear differential equation with distributed deviating argument. Our results improve and extend some known results in the literature. Some illustrating examples are also provided to show the importance of our results.