Boundary Value Problems for Integro-Differential Equations of Barbashin Type
J�rgen Appell, Anatolij S. Kalitvin, Petr P. Zabrejko · Journal of Integral Equations and Applications · 1994
In this paper we study linear integro-differential equations of Barbashin type, subject to appropriate boundary conditions.In particular, we show how to transform such equations to linear two-dimensional integral equations of second kind.This allows us to apply the classical Fredholm theory to obtain existence, uniqueness, and multiplicity results.Next, we apply a general fixed point principle in Knormed spaces to get more general existence results.Moreover, we employ weighted function spaces to cover the case of unbounded multiplicator functions.The abstract theorems are illustrated by means of an application to the problem of radiation propagation in physical systems.