Oscillation behavior of solutions of third-order nonlinear delay dynamic equations on time scales
Commun. Korean Math. Soc. 2011 Vol. 26, No. 3, 499-513
Printed September 1, 2011
Zhenlai Han, Tongxing Li, Shurong Sun, and Meng Zhang
Shandong University, University of Jinan, University of Jinan, University of Jinan
Abstract : By using the Riccati transformation technique, we study the oscillation and asymptotic behavior for the third-order nonlinear delay dynamic equations $$\left(c(t)\left(p(t)x^\Delta(t)\right)^\Delta\right)^\Delta+q(t)f(x(\tau(t)))=0$$ 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.
Keywords : oscillation behavior, third order delay dynamic equations, time scales
MSC numbers : 39A21, 34C10, 34K11, 34N05
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