Problèmes aux limites pour des equations intégro-différentielles de type Barbachine

Abstract

We discuss existence and uniqueness of solutions of a non-stationary integro-differential equation of Barbashin type, subject to natural boundary conditions. We show that the boundary value problem may be reduced to either a linear Fredholm integral equation, or a system of two linear Volterra integral equations. In the latter case one may apply fixed point principles in K-normed spaces to prove solvability and continuous dependence.