Bounded and periodic solutions of integral equations

T. A. Burton; Bo Zhang

doi:10.4067/S0719-06462012000100006

Authors

T. A. Burton Northwest Research Institute 732 Caroline Street, Port Angeles, WA 98362, USA
Bo Zhang Department of Mathematics and Computer Science Fayetteville State University Fayetteville, NC 28301, USA

DOI:

https://doi.org/10.4067/S0719-06462012000100006

Keywords:

Integral Equations, Boundedness, Periodic Solutions, Liapunov Functions

Abstract

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 xËŠ + 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.