Qualitative behavior of solutions of some integro equation models

In this thesis study; Qualitative analyzes of the solutions of integral equations and Volterra integro-differential equation models were examined. Integro-differential equation models and the stability, limitation, etc. of the solutions of these equation models. Lyapunov's second method, which we used, was introduced by giving place to the basic definitions and theorems necessary for the determination of qualitative characteristics such as The qualitative properties of the solutions of various linear and non-linear integral equations were investigated using a flexible Lyapunov functional. Uniform stability was analyzed using Lyapunov functions in infinitely delayed nonlinear Volterra integro-differential equations. Strictly non-negative Lyapunov functionals were used to obtain sufficient conditions that guarantee the exponential asymptotic stability and uniform exponential asymptotic stability of the zero solution of nonlinear functional differential systems.