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

摘要

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