N. V. Azbelev and L. F. Rakhmatullina

Theory of Linear Abstract Functional Differential Equations and Applications

The boundary value problem is considered for the abstract functional differential equation $Lx=f$, where $L:D\to B$ is a linear operator, $B$ is a Banach space, and $D$ is isomorphic to the direct product $B\times R^n$. The Green operator is constructed, continuous dependence on parameters is studied. The obtained results are applied to ordinary, impulse and singular equations.

Mathematics Subject Classification: 34K10.

Key words and phrases: Linear operator, Green operator, Noether operator, boundary value problem.