Oscillation Of Third-order Neutral Nonlinear Delay Dynamic Equations On Time Scales

This paper studies the oscillation of third-order delayed neutral dynamic equations on the time scales (?) and (?).It will obtain some theorems and inferences based on Riccati transformation,inequalities and related lemmas.When the study of equation satisfies the conditions of the theorem,all solutions to the equation are either oscillation or(?).Finally,specific examples are used to illustrate the relevant results.The equations studied in this paper are based on the oscillation of the third-order neutral dynamic equation (?) studied by Yang and the oscillation of the equation (?) studied by Li.apower for y~?(t) and x(?(t)) in the equations proposed by Yang and Li.When ?=1,the equations studied in this paper are the equations studied by Yang and Li.When ??1,new equations are obtained.We find the oscillation conditions of this equation.