Existence Theorems with Convexity Assumptions

  • Leonard D. Berkovitz
Part of the Applied Mathematical Sciences book series (AMS, volume 12)


In this chapter we develop the basic existence theorems for problems in which a certain convexity condition is present. The key theorem on which the entire development is based is Theorem 4.1, which guarantees compactness of certain sets of trajectories together with a property related to lower-semicontinuity. Theorem 4.1 will also be used in Chapters 4 and 6.


State Equation Existence Theorem Lower Semicontinuous Admissible Control Admissible Pair 


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Copyright information

© Springer Science+Business Media New York 1974

Authors and Affiliations

  • Leonard D. Berkovitz
    • 1
  1. 1.Division of Mathematical SciencesPurdue UniversityWest LafayetteUSA

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