Communications of the
Korean Mathematical Society
CKMS

ISSN(Print) 1225-1763 ISSN(Online) 2234-3024

Article

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Commun. Korean Math. Soc. 2011; 26(2): 197-205

Printed June 1, 2011

https://doi.org/10.4134/CKMS.2011.26.2.197

Copyright © The Korean Mathematical Society.

Oscillation of one order neutral differential equation with impulses

Jinfa Cheng and Yuming Chu

Xiamen University, Huzhou Teachers College

Abstract

Explicit sufficient conditions are established for the oscillation of the one order neutral differential equations with impulsive \[ (x(t)+ \sum\limits_{i = 1}^n {c_i } x(t-\sigma_i))' + px(t - \tau ) = 0,\ t \ne t_k , \] \[ \Delta (x(t_k )+ \sum\limits_{i = 1}^n {c_i } x(t_k-\sigma_i)) + p_0 x(t_k - \tau ) = 0, \] where $c_i \ge 0, i=1,2,\ldots,n, p\tau>0,p_0\tau>0,\Delta(x_k)=x(t_k^+)-x(t_k).$ Explicit sufficient and necessary condition are established when $c_i=0, i=1,2,\ldots,n$.

Keywords: oscillation, impulses, characteristic system

MSC numbers: 34A37