OSCILLATION OF ONE ORDER NEUTRAL DIFFERENTIAL EQUATION WITH IMPULSES

Title & Authors
OSCILLATION OF ONE ORDER NEUTRAL DIFFERENTIAL EQUATION WITH IMPULSES
Cheng, Jinfa; Chu, Yuming;

Abstract
Explicit sufficient conditions are established for the oscillation of the one order neutral differential equations with impulsive $\small{(x(t)+{\sum\limits^n_{i=1}}c_ix(t-{\sigma}_i))$, $\small{t{\neq}t_{\kappa}}$, $\small{{\Delta}(x(t_{\kappa})+{\sum\limits^n_{i=1}}c_ix(t_{\kappa}-{\sigma}_i))+p_0x(t_{\kappa}-{\tau})=0}$, $\small{c_i{\geq}0}$, $\small{i=1,2,{\ldots}n}$, $\small{p{\tau}}$>0, $\small{p_0{\tau}}$>0, $\small{{\Delta}(x_{\kappa})=x(t^+_{\kappa})-x(t_{\kappa})}$. Explicit sufficient and necessary condition are established when $\small{c_i}$ = 0, i = 1, 2, $\small{{\ldots}}$, n.
Keywords
oscillation;impulses;characteristic system;
Language
English
Cited by
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