Resumo

BURTON, T. A  e  ZHANG, Bo. Bounded and Periodic Solutions of Integral Equations. Cubo [online]. 2012, vol.14, n.1, pp. 55-79. ISSN 0719-0646.  http://dx.doi.org/10.4067/S0719-06462012000100006.

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.

Palavras-chave : Integral Equations; Boundedness; Periodic Solutions; Liapunov Functions.