Oscillation of one order neutral differential equation with impulses
Commun. Korean Math. Soc. 2011 Vol. 26, No. 2, 197-205
https://doi.org/10.4134/CKMS.2011.26.2.197
Printed June 1, 2011
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
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