Bounded and periodic solutions of integral equations
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T. A. Burton
taburton@olypen.com
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Bo Zhang
bzhang@uncfsu.edu
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DOI:
https://doi.org/10.4067/S0719-06462012000100006Abstract
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.
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Published
2012-03-01
How to Cite
[1]
T. A. Burton and B. Zhang, “Bounded and periodic solutions of integral equations”, CUBO, vol. 14, no. 1, pp. 55–79, Mar. 2012.
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