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Invariance for Contingent Equations

  • James A. Yorke
Part of the Lecture Notes in Operations Research and Mathematical Economics book series (LNE, volume 11/12)

Abstract

Let U be an open subset of R×Rd, and let f: U → Rd be continuous. For (t, x) ∈ U let Ω (t, x) ⊂ Rd be a non-empty closed set. We say Ω is compactly upper semi-continuous if for each compact Q ⊂ U, {(v, t, x): v ∈ Ω(t, x) and (t, x) ∈ U} ⊂ Rd × U is compact. We are interested in
$$ \dot x = f(t,x), $$
(E)
,
$$ \dot x \in \Omega \left( {t,x} \right). $$
(C)
.

Keywords

Ordinary Differential Equation Game Theory Open Subset Maximum Principle Stability Theory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Bibliography

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Copyright information

© Springer-Verlag Berlin Heidelberg 1969

Authors and Affiliations

  • James A. Yorke

There are no affiliations available

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