Oscillation Criteria for a Second Order Half-Linear Differential Equation with Delay, with Monotone Nondecreasing Delay Function.

Oscillation theory of different types of the differential equations is widely used today not only in mathematical disciplines, but also in almost all technical sciences. A large number of papers has been published in the field of nuclear physics and the theory of chemical reactions, which contains at least a part of the theory of oscillatory differential equations. It has a special application in fluid mechanics, which is confirmed by numerous studies and scientific gatherings organized by faculties and institutes that study this field of science, due to the exchange of results in the oscillation criteria special types of differential equations. This paper extends the study from Bojiičić and Jovanović (2019) which deals with the study of oscillation criteria for half-linear differential equation with delay. The known criteria of oscillation with weight averaging are derived in the case when the delay function is monotonically nondecreasing. Adequate examples are given to illustrate the validity of these criteria.