Generalized solution of boundary value problem with an inhomogeneous boundary condition

Abstract

A solution to boundary value problem is investigated for a controlled oscillation process,described by Fredholm integro-differential equation with inhomogeneous boundary conditions.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. Approximatesolutions of the boundary value problem are determined and their convergence to the exactsolution is proved.