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OSCILLATION BEHAVIOR OF SOLUTIONS OF THIRD-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES

  • Han, Zhenlai (School of Science University of Jinan, School of Control Science and Engineering Shandong University) ;
  • Li, Tongxing (School of Science University of Jinan) ;
  • Sun, Shurong (School of Science University of Jinan) ;
  • Zhang, Meng (School of Science University of Jinan)
  • Received : 2009.04.27
  • Published : 2011.07.31

Abstract

By using the Riccati transformation technique, we study the oscillation and asymptotic behavior for the third-order nonlinear delay dynamic equations $(c(t)(p(t)x^{\Delta}(t))^{\Delta})^{\Delta}+q(t)f(x({\tau}(t)))=0$ on a time scale 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

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