The persistence of nonoscillatory solutions of difference equations under impulsive perturbations (Q814110)

A sufficient condition for the persistence of nonoscillatory solutions of the difference equation of the form \[ x\left( t+\tau \right) -x\left( t\right) +\sum_{i=1}^{m}p_{i}\left( t\right) x\left( t-\gamma _{i}\tau \right) =0, \] under the impulsive perturbations, \[ x\left( t_{k}+\tau \right) -x\left( t_{k}\right) =I_{k}\left( x\left( t_{k}\right) \right) ,\text{ }k\in N\left( 1\right) \] is established. An example illustrating the results is given.