Roman K. Periodic and asymptotically periodic solutions of system of differential-functional equations of neutral type and their properties

The differential functional equations have been the object of the investigation by many mathematicians. The uniqueness and the beauty of solutions of such equations and also the wide use, which find such equations under the learning of real process, helped the active development of the theory of the differential functional equations as a whole. Thanks to it in this moment there is the whole row of the fundamental monographs in which the base of the theory of such equations have been developed and there are the new methods of the development of the differential functional equations and the perspective directions of further development of their theory are fixed. Especially, the questions about the existence of the limited periodical solutions of the wide classes of such equations aren't enough learned and also the learning of their characteristics. The examination of these questions has an important meaning for the following development of the differential functional equations' theory with the digression argument. Taking into consideration in the dissertation are developed the questions of the periodical solution systems of the differential functional equations neutral type. Especially, it was established the condition of existence and the periodical solution's unity of the wide class of such system equations. The researched asymptotic characteristics of the uninterrupted differential solutions are found in the circle of the constructed periodical solution. It was obtained the condition of the existence periodical solutions of the integral different equations and have been proposed the method of the constructions of such solutions. Have been got the condition of existence limited under $t