Oscillation behavior of solutions of third-order nonlinear delay dynamic equations on time scales

摘要

By using the Riccati transformation technique, we study the oscillation and asymptotic behavior for the third-order nonlinear delay dynamic equations $$left(c(t)left(p(t)x^Delta(t)ight)^Deltaight)^Delta+q(t)f(x(au(t)))=0$$ on a time scale $mathbb{T}$, where $c(t)$, $p(t)$ and $q(t)$ are real-valued positive rd-continuous functions defined on $mathbb{T}$. We establish some new sufficient conditions which ensure that every solution oscillates or converges to zero. Our oscillation results are essentially new. Some examples are considered to illustrate the main results.