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 xˊ + 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.
@article{1354,
title = {Bounded and Periodic Solutions of Integral Equations},
journal = {CUBO, A Mathematical Journal},
volume = {14},
year = {2012},
language = {en},
url = {http://dml.mathdoc.fr/item/1354}
}
Burton, T. A.; Zhang, Bo. Bounded and Periodic Solutions of Integral Equations. CUBO, A Mathematical Journal, Tome 14 (2012) . http://gdmltest.u-ga.fr/item/1354/