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Handbook of Multivalued Analysis

Volume II: Applications

  • Book
  • © 2000

Overview

Authors:
  1. Shouchuan Hu

    1. Mathematics Department, Southwest Missouri State University, Springfield, USA

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    You can also search for this author in PubMed   Google Scholar

  2. Nikolas S. Papageorgiou

    1. Department of Mathematics, National Technical University, Athens, Greece

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    You can also search for this author in PubMed   Google Scholar

Part of the book series: Mathematics and Its Applications (MAIA, volume 500)

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Table of contents (17 chapters)

  1. Front Matter

    Pages i-xi
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  2. Evolution Inclusions Involving Monotone Coercive Operators

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 1-114

  3. Evolution Inclusions of the Subdifferential Type

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 115-204

  4. Special Topics in Differential and Evolution Inclusions

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 205-350

  5. Optimal Control

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 351-508

  6. Calculus of Variations

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 509-593

  7. Mathematical Economics

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 595-704

  8. Stochastic Games

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 705-790

  9. Special Topics in Mathematical Economics and Optimization

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 791-862

  10. Erratum

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 926-926

  11. Erratum to: Evolution Inclusions of the Subdifferential Type

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925

  12. Erratum to: Optimal Control

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925

  13. Erratum to: Mathematical Economics

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925

  14. Erratum to: Evolution Inclusions Involving Monotone Coercive Operators

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925

  15. Erratum to: Special Topics in Differential and Evolution Inclusions

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925

  16. Erratum to: Calculus of Variations

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925

  17. Erratum to: Stochastic Games

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925

  18. Erratum to: Special Topics in Mathematical Economics and Optimization

    • Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 926-926

  19. Back Matter

    Pages 863-932
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Keywords

About this book

In volume I we developed the tools of "Multivalued Analysis. " In this volume we examine the applications. After all, the initial impetus for the development of the theory of set-valued functions came from its applications in areas such as control theory and mathematical economics. In fact, the needs of control theory, in particular the study of systems with a priori feedback, led to the systematic investigation of differential equations with a multi valued vector field (differential inclusions). For this reason, we start this volume with three chapters devoted to set-valued differential equations. However, in contrast to the existing books on the subject (i. e. J. -P. Aubin - A. Cellina: "Differential Inclusions," Springer-Verlag, 1983, and Deimling: "Multivalued Differential Equations," W. De Gruyter, 1992), here we focus on "Evolution Inclusions," which are evolution equations with multi­ valued terms. Evolution equations were raised to prominence with the development of the linear semigroup theory by Hille and Yosida initially, with subsequent im­ portant contributions by Kato, Phillips and Lions. This theory allowed a successful unified treatment of some apparently different classes of nonstationary linear par­ tial differential equations and linear functional equations. The needs of dealing with applied problems and the natural tendency to extend the linear theory to the nonlinear case led to the development of the nonlinear semigroup theory, which became a very effective tool in the analysis of broad classes of nonlinear evolution equations.

Authors and Affiliations

  • Mathematics Department, Southwest Missouri State University, Springfield, USA

    Shouchuan Hu

  • Department of Mathematics, National Technical University, Athens, Greece

    Nikolas S. Papageorgiou

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