Oscillation Criteria of Certain Third-Order Differential Equation with Piecewise Constant Argument

Abstract

We study the oscillation and asymptotic behavior of third-order nonlinear delay differential equation with piecewise constant argument of the form $(r_2(t)(r_1(t)x\text{'}(t))\text{'})\text{'}+p(t)x\text{'}(t)+f(t,x([t]))=0$. We establish several sufficient conditions which insure that any solution of this equation oscillates or converges to zero. Some examples are given to illustrate the importance of our results.