Abstract
We establish existence of a continuous selection of multifunctions associated with quantum stochastic evolution inclusions under a general Lipschitz condition. The coefficients here are multifunctions but not necessarily Lipschitz.
Highlights
Existence of continuous selections of multifunctions associated with the sets of solutions of Lipschitzian and non-Lipschitzian quantum stochastic differential inclusions (QSDIs) has been considered in [2, 8], while the existence of solution of quantum stochastic evolution arising from hypermaximal monotone coefficients was established in [9]
In [10, 11] several results have been established concerning some properties of the solution sets of QSDIs
Results concerning the topological properties of solution sets of Lipschitzian QSDI were considered in [12]
Summary
In [1], results on continuous selections of solution sets of quantum stochastic evolution inclusions (QSEIs) were established under the Lipschitz condition defined in [2, 13]. In order to generalize the results in the literature concerning QSDI, in [8] existence of continuous selections of solutions sets of non-Lipschitzian quantum stochastic differential inclusions was considered.
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