Degree theory for perturbations of m-accretive operators generating compact semigroups with constraints

In the paper a topological degree is constructed for the class of maps of the form - A + F where M is a closed neighborhood retract in a Banach space E, A : D(A) is a m-accretive map such that - A generates a compact semigroup and F : M -> E is a locally Lipschitz map. The obtained degree is applied to studying the existence and branching of periodic points of differential inclusions of the type {(u) over dot is an element of -lambda Au + lambda F(t, u), lambda < 0 {u(t) is an element of M {u(0) = u(T).