Bounded and Periodic Solutions of Integral Equations
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.
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| Main Authors: | , |
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| Format: | Digital revista |
| Language: | English |
| Published: |
Universidad de La Frontera. Departamento de Matemática y Estadística.
2012
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| Online Access: | http://www.scielo.cl/scielo.php?script=sci_arttext&pid=S0719-06462012000100006 |
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