Handbook of Multivalued Analysis

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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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.

• Applied Mathematics
• Calculus of Variations
• Finite
• Optimal control
• Topology
• calculus
• function
• functional analysis
• mathematics
• optimization
• partial differential equations

• 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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