In this paper we introduce a new concept of generalized solutions generalizing the notion of relaxed solutions recently introduced by Fattorini. We present some results on the question of existence of generalized or measure valued solutions for semilinear evolution equations on Banach spaces with polynomial nonlinearities. The results are illustrated by two examples one of which arises in nonlinear quantum mechanics. The results are then applied to some control problems.
In this paper, we consider a class of infinite dimensional stochastic impulsive evolution inclusions driven by vector measures. We use stochastic vector measures as controls adapted to an increasing family of complete sigma algebras and prove the existence of optimal controls.
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