• 제목/요약/키워드: third order delay dynamic equations

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

  • Han, Zhenlai;Li, Tongxing;Sun, Shurong;Zhang, Meng
    • 대한수학회논문집
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    • 제26권3호
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    • pp.499-513
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    • 2011
  • 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.