Topological degree methods in boundary value problems for degenerate functional differential inclusions with infinite delay

We consider the general boundary value problem for a degenerate semilinear functional differential inclusion in a Banach space with infinite delay. We construct the multivalued integral operator whose fixed points are mild solutions of the above problem and study its properties. We apply the topological degree method to obtain the general existence principle and consider some particular cases, including Cauchy and periodic problems.