THE JUSTIFICATION OF THE TRUNCATION APPLIED TO INHOMOGENEOUS INTEGRAL EQUATIONS WITH CAUCHY’S KERNEL

Abstract

Let us consider the following Sturm-Liouville problem: To find the values of and the functions odd with respect to , such that. The restriction is Hölder-continuous function at the points where the boundary conditions change while can at most be a piecewise continuous function. Following the technique and procedure of [1] closely, the solutions, odd with respect to , of problem (1) are found to be where stand for the eigenvalues and and the complex Fourier components of the function vanishing on the intervals and compatible with the third condition of .