Generalized solution of boundary value problem with an inhomogeneous boundary condition

Abstract

In this problem, we study the solution to boundary value problem for a controlled oscillation process, described by Fredholm integro-differential equation with an inhomogeneous boundary condition. An algorithm is developed for constructing a generalized solution of boundary value problem. It is proved that a weak generalized solution is an element of Hilbert space. Approximate solutions of the boundary value problem are determined and their convergence is proved.