Abstract. We introduce the notion of variational (semi-) strict quasimonotonicity for a multivalued operator T : X ⇒ X * relative to a nonempty subset A of X which is not necessarily included in the domain of T . We use this notion to characterize the subdifferentials of continuous (semi-) strictly quasiconvex functions. The proposed definition is a relaxation of the standard definition of (semi-) strict quasimonotonicity, the latter being appropriate only for operators with nonempty values. Thus, the derived results are extensions to the continuous case of corresponding results for locally Lipschitz functions.
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