Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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OSCILLATION OF ONE ORDER NEUTRAL DIFFERENTIAL EQUATION WITH IMPULSES

  • Cheng, Jinfa (Department of Mathematics Xiamen University) ;
  • Chu, Yuming (Department of Mathematics Huzhou Teachers College)
  • Received : 2007.06.26
  • Published : 2011.04.30
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Abstract

Explicit sufficient conditions are established for the oscillation of the one order neutral differential equations with impulsive $(x(t)+{\sum\limits^n_{i=1}}c_ix(t-{\sigma}_i))'+px(t-{\tau})=0$, $t{\neq}t_{\kappa}$, ${\Delta}(x(t_{\kappa})+{\sum\limits^n_{i=1}}c_ix(t_{\kappa}-{\sigma}_i))+p_0x(t_{\kappa}-{\tau})=0$, $c_i{\geq}0$, $i=1,2,{\ldots}n$, $p{\tau}$>0, $p_0{\tau}$>0, ${\Delta}(x_{\kappa})=x(t^+_{\kappa})-x(t_{\kappa})$. Explicit sufficient and necessary condition are established when $c_i$ = 0, i = 1, 2, ${\ldots}$, n.

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References

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