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Cubo (Temuco)

versão On-line ISSN 0719-0646


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.

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.

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