Summary
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 functionf 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→(H) is a multifunction satisfying some regularity assumptions.
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Cardinali, T., Papalini, F. Existence theorems for nonlinear evolution inclusions. Annali di Matematica pura ed applicata 173, 1–11 (1997). https://doi.org/10.1007/BF01783459
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DOI: https://doi.org/10.1007/BF01783459