Existence theorems for nonlinear evolution inclusions

In this paper we obtain an existence theorem for the abstract Cauchy problem for multivalued differential equations of the form u′∈ - ∂-f(u) + G(u), u(O) = x0, where ∂-f is the Fréchet subdifferential of a function f defined on an open subset Ω of a real separable Hilbert space H, taking its values in R ∪ {+ ∞} and G is a multifunction from C([0, T], Ω) into the nonempty subsets of L2([0, T], H). As an application we obtain an existence theorem for the multivalued perturbed problem x′∈ - ∂-f(x) + F(t, x), x(0) = x0, where F:[0, T] × Ω → n(H) is a multifunction satisfying some regularity assumptions.