Oscillation criteria for third order nonlinear delay dynamic equations on time scales
Volume 99 / 2010
Annales Polonici Mathematici 99 (2010), 143-156
MSC: 34C10, 34K11, 34N05, 39A21.
DOI: 10.4064/ap99-2-3
Abstract
By means of Riccati transformation technique, we establish some new oscillation criteria for third-order nonlinear delay dynamic equations $$ ((x^{\Delta\Delta}(t))^\gamma)^\Delta+p(t)x^\gamma(\tau(t))=0 $$ on a time scale $\mathbb{T};$ here $\gamma>0$ is a quotient of odd positive integers and $p$ a real-valued positive rd-continuous function defined on $\mathbb{T}.$ Our results not only extend and improve the results of T. S. Hassan [Math. Comput. Modelling 49 (2009)] but also unify the results on oscillation of third-order delay differential equations and third-order delay difference equations.
