Six integral equations and a flexible Liapunov functional

In this paper we study several integral equations including linear, nonlinear, and resolvent equations, by means of a flexible Liapunov functional. The goal is to obtain qualitative properties involving limit sets of solutions. The Liapunov functional is first applied directly to the integral equations without first differentiating the integral equation. In addition we develop a strategy for converting an integral equation into a strongly stable differential equation which maintains most of the properties of the kernel and then we apply that flexible Liapunov functional to it. None of this is applied to singular kernels, but work is in progress to apply the Liapunov functional to equations having singular kernels.