Abstract
Inf-compactness of the objective functional in an abstract variational problem, where the dynamical system consists of a linear functional-integral equation, is proven by suitably topologizing the space of relaxed control functions. The topology is obtained quite naturally from a Hilbert cube compactification of the space of control points. Under additional convexity assumptions a general existence result, implying that of A. D. Ioffe ( Dokl. Akad. Nauk SSSR 205 (1972), 277–280; Soviet Math. Dokl. 13 (1972), 919–923) is proven.
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