Oscillation Criteria For A Class Of Half-linear Emden-fowler Functional Differential Equations Of Neutral Type

The theory of the oscillation of functional differential equations is a ne w discipline.With the development of science,many fields require the theory of differential equations as the theoretical support.Every scholar has also persistently worked hard.Over the past century,various scholars have continuously improved the existing conclusions.Extending the original problem-solving ideas,studying the vibrational theory of differential equations,giving more significance to the vibration theory of differential equations,and applying it to the development of science and technology,with practical value.For example,Hutchinson(1948)established a time-delayed Logistic differential equation(?)this equation is related to biological populations,where?represents the impact of external factors on population growth,such as the incubation period of animals,changes in living conditions,the probability of mammalian conception,and Pregnancy time and so on all have an impact on biological populations and cause vibrational changes.The oscillation of the differential equation solution is one of the important properties of the solution of the differential equation.It has applications in many fields,especially the solution to the problem of the vibration scheme.In recent decades,the theory has developed rapidly and has received extensive attention.In this thesis,the oscillation of a class of neutral(?),with a free term is discussed.The oscillation criterion of the equation is discussed when the value of e(t)changes.