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Turnpike theorem for a class of differential inclusions arising in economic dynamics. (English) Zbl 0923.49006
The paper is devoted to the study of asymptotic behavior of trajectories to a differential inclusion $\dot x (t) \in b(x(t)) -x(t)$ with $b(x)$ being a superlinear set-valued map. The motivations for the above model to be studied may be found in economic dynamics. The author establishes the turnpike property for a wider class of superlinear mappings (without the assumption of the strict convexity of their graphs). For a space of superlinear mappings describing continuous multisector models the existence of an open everywhere dense subset $E$ of mappings with turnpike property is also proved. The main result is the generalization of previous investigations of the author [Optimization 19, No. 3, 427-441 (1988; Zbl 0645.90010)].
49J24Optimal control problems with differential inclusions (existence) (MSC2000)
91B62Growth models in economics
34A60Differential inclusions
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