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Handbook of Multivalued Analysis

Volume II: Applications

  • Shouchuan Hu
  • Nikolas S. Papageorgiou

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

Table of contents

  1. Front Matter
    Pages i-xi
  2. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 1-114
  3. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 115-204
  4. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 205-350
  5. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 351-508
  6. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 509-593
  7. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 595-704
  8. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 705-790
  9. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 791-862
  10. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925
  11. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925
  12. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925
  13. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925
  14. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925
  15. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925
  16. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 925-925
  17. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 926-926
  18. Shouchuan Hu, Nikolas S. Papageorgiou
    Pages 926-926
  19. Back Matter
    Pages 863-932

About this book

Introduction

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.

Keywords

Applied Mathematics Calculus of Variations Finite Optimal control Topology calculus function functional analysis mathematics optimization

Authors and affiliations

  • Shouchuan Hu
    • 1
  • Nikolas S. Papageorgiou
    • 2
  1. 1.Mathematics DepartmentSouthwest Missouri State UniversitySpringfieldUSA
  2. 2.Department of MathematicsNational Technical UniversityAthensGreece

Bibliographic information