Handbook of Multivalued Analysis: Volume II: Applications

Shouchuan Hu, Nikolas S. Papageorgiou (auth.)0792361644, 9780792361640, 0792346831, 0792346823

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.

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Table of contents :
Front Matter….Pages i-xi
Evolution Inclusions Involving Monotone Coercive Operators….Pages 1-114
Evolution Inclusions of the Subdifferential Type….Pages 115-204
Special Topics in Differential and Evolution Inclusions….Pages 205-350
Optimal Control….Pages 351-508
Calculus of Variations….Pages 509-593
Mathematical Economics….Pages 595-704
Stochastic Games….Pages 705-790
Special Topics in Mathematical Economics and Optimization….Pages 791-862
Erratum to: Evolution Inclusions Involving Monotone Coercive Operators….Pages 925-925
Erratum to: Evolution Inclusions of the Subdifferential Type….Pages 925-925
Erratum to: Special Topics in Differential and Evolution Inclusions….Pages 925-925
Erratum to: Optimal Control….Pages 925-925
Erratum to: Calculus of Variations….Pages 925-925
Erratum to: Mathematical Economics….Pages 925-925
Erratum to: Stochastic Games….Pages 925-925
Erratum to: Special Topics in Mathematical Economics and Optimization….Pages 926-926
Erratum….Pages 926-926
Back Matter….Pages 863-932