Initial value methods in the theory of Fredholm integral equations III. The nonlinear eigenvalue problem

摘要

In this paper, it is shown that the method introduced recently by Kalaba and Scott for solving nonlinear characteristic value problems for integral operators is equivalent to a nonlinear characteristic value problem for a matrix. This is demonstrated by finding the explicit solution to the set of differential equations used by them. The results generalize those proved recently by the author for the linear problem.