On the qualitative analysis of solutions of some equation models

This thesis consists of ten chapters. In the first chapter of this thesis, some works related to subject of thesis are briefly summarized. In the second chapter of this thesis, the materials and methods used in the thesis were notified. In the third chapter of the thesis, some basic information and concepts related to the subject of the thesis were given. In Chapter 4, the asymptotic stability, uniform stability and integrability of the solutions of a certain system of non-linear VIDD were studied by the LRM and two examples were given. In Chapter 5, by means of the Lyapunov's second method, stability, uniform stability, asymptotic stability and integrability of the solutions of a non-linear system of VIDD with constant delay were discussed and two examples were given. Chapter 6, the boundedness and square integrability of the solutions of a certain scalar VIDD with constant delay by means of the LRM and an example was given. In Chapter 7, a scalar VIDD with infinite delay was considered. Stability and uniform stability of zero solution, integrability and absolute integrability of non-zero solutions of VIDD were investigated by the second method of Lyapunov and an example was given. In Chapter 8, we investigated asymptotic stability and uniform stability of zero solution, integrability and boundedness at infinity of non-zero solutions of a certain non-linear system of VIDD with constant delay. In Chapter 9 it was investigated the same concepts as in previous chapter to a nonlinear systems of VIDD with time variable delay by using the LRM and two specific examples were given. In Chapter 10, a detailed conclusion of thesis was given.