Boundary value problem for abstract first order differential equation with integral condition

The present paper is devoted to the study of a boundary value problem for abstract first order linear differential equation with integral boundary conditions. We obtain necessary and sufficient conditions for the unique solvability and well-posedness. We also study the Fredholm solvability. Finally, we obtain a result of the stability of solution with respect to small perturbation. © 2006 Elsevier Inc. All rights reserved.