Existence and uniqueness of solutions of Abel integral equations with power-law non-linearities

摘要

In this article a class of nonlinear Abel-type integral equations is studied. These equations have at least the trivial solution, but we are interested in a continuous, positive solution. We show that there exists a unique positive solution in an order interval of a cone in a Banach space. (c) 2005 Elsevier Ltd. All rights reserved.