New Oscillatory Theorems for Third-Order Nonlinear Delay Dynamic Equations on Time Scales

This paper is concerned with the oscillatory properties of the third-order nonlinear delay dynamic equations of the form  on time scales , where  is a quotient of odd positive integers. Applying the inequality technique we present two new sufficient conditions which ensure that every solution of equations is oscillatory or converges to zero. The results obtained improve and complement some known results in the literature.