Journal of applied mathematics & informatics

The Korean Society for Computational and Applied Mathematics (한국전산응용수학회)
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ON THE OSCILLATION OF SECOND-ORDER NONLINEAR DELAY DYNAMIC EQUATIONS ON TIME SCALES

  • Zhang, Quanxin (Department of Mathematics and Information Science, Binzhou University) ;
  • Sogn, Xia (Department of Mathematics and Information Science, Binzhou University) ;
  • Gao, Li (Department of Mathematics and Information Science, Binzhou University)
  • Received : 2011.03.17
  • Accepted : 2011.06.10
  • Published : 2012.01.30
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Abstract

By using the generalized Riccati transformation and the inequality technique, we establish some new oscillation criterion for the second-order nonlinear delay dynamic equations $$(a(t)(x^{\Delta}(t))^{\gamma})^{\Delta}+q(t)f(x({\tau}(t)))=0$$ on a time scale $\mathbb{T}$, here ${\gamma}{\geq}1$ is the ratio of two positive odd integers with $a$ and $q$ real-valued positive right-dense continuous functions defined on $\mathbb{T}$. Our results not only extend and improve some known results, but also unify the oscillation of the second-order nonlinear delay differential equation and the second-order nonlinear delay difference equation.

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References

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