Bounded and Periodic Solutions of Integral Equations

in this paper we introduce a new method for obtaining boundedness of solutions of integral equations. from the integral equation we form an integrodifferential equation by computing x' + kx to which we apply a liapunov functional. this can be far more effective than the usual technique of differentiating the equation. the qualitative properties derived from that equation are then transferred to a majorizing function for the integral equation. schaefer's fixed point theorem is used to conclude that there is a periodic solution. three kinds of integral equations are studied and they are shown to be related through two examples.