# Article

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Keywords:
evolution triple; compact embedding; pseudomonotone operator; demicontinuity; coercive operator; dominated convergence theorem
Summary:
In this paper we prove the existence of periodic solutions for a class of nonlinear evolution inclusions defined in an evolution triple of spaces $(X,H,X^{*})$ and driven by a demicontinuous pseudomonotone coercive operator and an upper semicontinuous multivalued perturbation defined on $T\times X$ with values in $H$. Our proof is based on a known result about the surjectivity of the sum of two operators of monotone type and on the fact that the property of pseudomonotonicity is lifted to the Nemitsky operator, which we prove in this paper.
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