Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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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
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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.

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References

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