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OSCILLATION OF ONE ORDER NEUTRAL DIFFERENTIAL EQUATION WITH IMPULSES

OSCILLATION OF ONE ORDER NEUTRAL DIFFERENTIAL EQUATION WITH IMPULSES

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