  A fairly general continuation theorem of Leray-Schauder type for the class of
so-called admissible multimaps is set forth. This result is then used to
establish a universal rule for solving operator inclusions of Hammerstein type
in Lebesgue-Bochner spaces. Examples illustrating the legitimacy of this
approach include the initial value problem for perturbation of $m$-accretive
mutivalued differential equations, the anti-periodic problem for semilinear
differential inclusions, abstract integral inclusions of Fredholm and Volterra
type and the two-point boundary value problem for nonlinear evolution
inclusions.
