Some stability criteria for Volterra integro – differential equations

This master thesis consists of seven chapters, Chapters 1-7. In first chapter of the thesis, some short information were given about some methods which are available in the literature and can also be used to get information on the qualitative behaviors of solutions of integro-differential equations under investigation without solving them. In the second chapter of this thesis, some scientific works, which are related to the subject of this thesis and can be found in the literature, were summarized. In Chapter 3, the material-method used in this thesis was presented. Chapter 4 includes some basic information such as definitions, theorems and so on, which are related to the subject of this thesis. In Chapter 5 of this thesis, some qualitative results were given on the convergence, integrability, square integrability, stability, boundedness, uniform stability, asymptotic stability, uniform asymptotic stability and instability of solutions of Volterra integro-differential equations and systems amd their perturbed form, convolution and non-convolution type Volterra integro-differential equations and systems. In Chapter 5, some examples were given on the subject. In Chapter 6, some theorems, which contain sufficient conditions on the uniformly asymptotically stability of solutions of certain a linear differential equation system with multiple constant delays, nonlinear Volterra integro-differential equations first order with variable delay, non-linear Volterra integro-differential equations first order with constant delay and so on were given. At the end, a discussion and conclusion about the studies done in this thesis was given.