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

Abstract.

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 $E, A : D(A) \multimap E$ 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

$$ \left\{ \begin{aligned} &\dot{u} \in - \lambda Au + \lambda F(t,u),\lambda > 0\\ & u(t) \in M\\ & u(0) = u(T).\\ \end{aligned} \right. $$