| Our objective in this work is to obtain existence results for functional differential equations involving abstract Volterra operators. Existence of a unique solution, continuous dependence of solutions with respect to data and integral representation of solutions have been established for first order linear functional differential equations involving abstract Volterra operators. We have obtained the existence of a solution for nonlinear boundary value problems involving abstract Volterra operators. Existence of a unique solution has also been established for second order nonhomogeneous linear abstract Volterra functional differential equations. Finally, as an application of the general results established in our work, we have obtained the existence of a unique solution for a class of integro-differential systems which occurs in System Theory. |
