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Abstract

Given a Cauchy problem dx(t) in -(E_1(t,x(t))d Lambda_{pi}(t)+F_1(t,x(t))dA_f(t)+G_1(t,x(t))dA^+_g(t)+ H_1(t,x(t))dt) +(E_2(t,x(t))d Lambda_{pi}(t)+F_2(t,x(t))dA_f(t)+G_2(t,x(t))dA^+_g(t)+H_2(t,x(t))dt) x(0)=a, where E_1, F_1, G_1, H_1 are hypermaximal monotone multivalued maps and E_2, F_2, G_2, H_2 are Lipschitzian multifunctions. For each a, suppose the set of adapted weakly absolutely continuous quantum stochastic processes which are weak solutions of the Cauchy problem is S^T(a). We prove the existence of a continuous selection of the multifunction <eta,a xi> mapsto S^T(a)(eta, xi), the matrix elements of S^T(a).

How to Cite this Article:

M.O. Ogundiran, Continuous selections of solution sets of quantum stochastic evolution inclusions, Journal of Nonlinear Functional Analysis 2014 (2014), Article ID 4.