Etude d’un problème aux limites non régulier.

Abstract

In this work, we are interested to the study of boundary values problems with integral boundary conditions. We obtain the existence and uniqueness of solutions with a priori estimate, and prove the Fredholm solvability of the problem. Finally, we apply an iteration approximation method to approximate an initial condition of a boundary value problem for an abstract first order homogeneous linear differential equation with an integral boundary condition on a Banach space.