Invariance for Contingent Equations

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


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
$$ \dot x = f(t,x), $$
$$ \dot x \in \Omega \left( {t,x} \right). $$


Ordinary Differential Equation Game Theory Open Subset Maximum Principle Stability Theory 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1969

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  • James A. Yorke

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