Periodic solutions of neutral difference equations

For linear or convex neutral difference equations with finite delay and with infinite delay, the Massera-type theorems are established. That is, the necessary and sufficient condition for existence of a periodic solution is the existence of a bounded solution. In this way, the Massera theorem for the ordinary differential equations is extended to neutral difference equations. As immediate implications the corresponding new results for delay difference equations are obtained since the latter can be regarded as a special case of the former.