Linear integral equation

Summary

A linear integral equation is an integral equation in which the unknown function enters linearly, both outside and inside the integral. Its general form is $a(x) \varphi(x) = f(x) + \lambda \int K(x, s) \varphi(s) \, ds$ with a given kernel $K$. The solutions form an affine space, so linear algebra and operator theory apply. Fredholm and Volterra equations are the main classes.