Asymptotic stability of solutions of differential-difference equations

In this thesis, differential equations and their discrete forms containing specific classes of difference equations are discussed and some new results are obtained for asymptotic stability of these equations. The thesis consists of three parts. In the first part, information about the historical development process and application areas of the differential and difference equations discussed in thesis are given. In the second part, we remind the basic definitions and theorems related to differential and difference equations. The third part is the original part of this thesis, in the first section, asymptotic stability of some classes of linear, homogeneous difference equation systems with one delay is investigated and some examples are given. In the second section, asymptotic stability of some classes of linear, homogeneous difference equation systems is investigated with two delays and some examples are presented. In the third section, the asymptotic stability conditions of the nonlinear delayed difference equation system with variable delay are investigated and exemplified. In the last section, the asymptotic stability of the differential equations systems that correspond continuous functions of the difference equation systems in the second section is studied and some examples are given.