The general criteria of stability for equihbrium points of scalar autonomous difference equations are given, wich cover all the cases as long as the right-hand function has continuous derivatives up to the desired order. Thus, the stability problems of scalar autonomous difference equations are thoroughly solved. The proofs of the obtained criteria are mathematically rigorous and complete. Also, several exam pies are given to illustrate the obtained results.
A criterion for the existence of T-periodic solutions of functional differential equations with finite delay is established, in which the uniform boundedness of solutions has been removed from the conditions. The obtained result is the counterpart of the one recently obtained for infinite delay equations, but the conditions in this work are simplified and much easier to verify. Also, the proof has been improved to be more clear and compact.
