Abstract
Let a variable, closed, bounded, and convex subset ofX, a separable and reflexive Banach space, be denoted byG(t). Suppose thatG(t) varies upper-semicontinuously with respect to inclusion ast varies in [0,T]. We say that the strongly measurable mapu from [0,T] toX is an admissible control if, for almost everyt in [0,T],u(t) is an element ofU, a closed, bounded, and convex subset ofX, and ∥u∥ p ⩽M1p, where p>1 andM>0.
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