Bulletin of the Korean Mathematical Society (대한수학회보)

Korean Mathematical Society (대한수학회)
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COMPARISON THEOREMS ON THE OSCILLATION OF A CLASS OF NEUTRAL DIFFERENCE EQUATIONS WITH CONTINUOUS VARIABLES

  • Karpuz, Basak (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCES AND ARTS ANS CAMPUS) ;
  • Ocalan, Ozkan (DEPARTMENT OF MATHEMATICS FACULTY OF SCIENCES AND ARTS ANS CAMPUS)
  • Published : 2010.03.31
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Abstract

In this paper, we introduce an iterative method to study oscillatory properties of delay difference equations of the following form ${\nabla}_{\alpha}\;[x(t)\;-\;r(t)x(t\;-\;k)]\;+\;p(t)x(t\;-\;{\tau})\;-\;q(t)x(t\;-\;{\sigma})\;=\;0$, $t\;{\geq}\;t_0$, where $t_0\;{\in}\;\mathbb{R}$, t varies in the real interval ($t_0,\;{\infty}$), $\alpha$ > 0, $\kappa$, $\tau$, ${\sigma}\;{\geq}\;0$, $r\;{\in}\;C\;([t_0-{\alpha},\;{\infty}),\;\mathbb{R}^+$, p, $q\;{\in}\;C\;([t_0,\;{\infty}),\;\mathbb{R}^+)$ and ${\nabla}_{\alpha}x(t)\;=\;x(t)\;-\;x(t\;-\;{\alpha})$ for $t\;{\geq}\;t_0$.

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References

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