On the trajectories of generalized functional-differential systems of neutral type
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Some sufficient conditions are presented for the compactness of the set of all relaxed trajectories of generalized functional-differential equations of the form\(\dot x(t) \in F(t,x_t ,\dot x_t )\), whereF is a multivalued mapping, with values that are nonempty compact subsets of then-dimensional Euclidean space. Furthermore, it is shown that the set of all trajectories is dense in the set of all relaxed trajectories. Finally, some remarks on the application of the above results to optimization problems are given.
Key WordsOptimization problems functional-differential equations of neutral type existence theory
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