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.
Jinfa Cheng and Yuming Chu
Xiamen University, Huzhou Teachers College
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
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