Fredholm Integral Equations of the Second Kind (General Kernel)

Abstract

In Chap. 1, we conducted a thorough examination of the Fredholm integral equation of the second kind for an arbitrary complex parameter λ, assuming that the free term f(x) is complex-valued and continuous on the interval [a, b] and that the kernel K(x, t) is complex-valued, continuous, and separable on the square Q(a, b) = { (x, t): [a, b] ×[a, b]}. We stated the four Fredholm theorems and the Fredholm Alternative Theorem which provide for the construction of all possible solutions to the equation under these assumptions.