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This book is an attempt to give a systematic presentation of results and me- ods which concern the ?xed point theory of multivalued mappings and some of its applications. In selecting the material we have restricted ourselves to stu- ing topological methods in the ?xed point theory of multivalued mappings and applications, mainly to di?erential inclusions. Thus in Chapter III the approximation (on the graph) method in ?xed point theory of multivalued mappings is presented. Chapter IV is devoted to the ho- logical methods and contains more general results, e.g. the Lefschetz Fixed Point Theorem, the ?xed point index and the topological degree theory. In Chapter V applications to some special problems in ?xed point theory are formulated. Then in the last chapter a direct applications to di?erential inclusions are presented. Note that Chapters I and II have an auxiliary character, and only results c- nected with the Banach Contraction Principle (see Chapter II) are strictly related to topological methods in the ?xed point theory. In the last section of our book (see Section 75) we give a bibliographicalguide and also signalsome further results which are not contained in our monograph. The author thanks several colleagues and my wife Maria who read and c- mented on the manuscript. These include J. Andres, A. Buraczewski, G. Gabor, A. G´orka,M.Go´rniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph.
Fixed point theory. --- Set-valued maps. --- Many-valued mappings --- Mappings, Point-to-set --- Maps, Set-valued --- Multi-valued mappings --- Multivalued mappings --- Point-to-set mappings --- Mappings (Mathematics) --- Selection theorems --- Fixed point theorems (Topology) --- Nonlinear operators --- Coincidence theory (Mathematics) --- Mathematics. --- Topology. --- Algebraic topology. --- Operator theory. --- Differential Equations. --- Mathematics, general. --- Algebraic Topology. --- Operator Theory. --- Ordinary Differential Equations. --- 517.91 Differential equations --- Differential equations --- Functional analysis --- Topology --- Analysis situs --- Position analysis --- Rubber-sheet geometry --- Geometry --- Polyhedra --- Set theory --- Algebras, Linear --- Math --- Science --- Differential equations.
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Algebraic topology --- Topology --- Operator theory --- Differential equations --- Mathematics --- differentiaalvergelijkingen --- analyse (wiskunde) --- topologie (wiskunde) --- wiskunde --- topologie
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This book is an attempt to give a systematic presentation of results and me- ods which concern the ?xed point theory of multivalued mappings and some of its applications. In selecting the material we have restricted ourselves to stu- ing topological methods in the ?xed point theory of multivalued mappings and applications, mainly to di?erential inclusions. Thus in Chapter III the approximation (on the graph) method in ?xed point theory of multivalued mappings is presented. Chapter IV is devoted to the ho- logical methods and contains more general results, e.g. the Lefschetz Fixed Point Theorem, the ?xed point index and the topological degree theory. In Chapter V applications to some special problems in ?xed point theory are formulated. Then in the last chapter a direct applications to di?erential inclusions are presented. Note that Chapters I and II have an auxiliary character, and only results c- nected with the Banach Contraction Principle (see Chapter II) are strictly related to topological methods in the ?xed point theory. In the last section of our book (see Section 75) we give a bibliographicalguide and also signalsome further results which are not contained in our monograph. The author thanks several colleagues and my wife Maria who read and c- mented on the manuscript. These include J. Andres, A. Buraczewski, G. Gabor, A. G´orka,M.Go´rniewicz, S. Park and A. Wieczorek. The author wish to express his gratitude to P. Konstanty for preparing the electronic version of this monograph.
Algebraic topology --- Topology --- Operator theory --- Differential equations --- Mathematics --- differentiaalvergelijkingen --- analyse (wiskunde) --- topologie (wiskunde) --- wiskunde --- topologie
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This monograph gives a systematic presentation of classical and recent results obtained in the last couple of years. It comprehensively describes the methods concerning the topological structure of fixed point sets and solution sets for differential equations and inclusions. Many of the basic techniques and results recently developed about this theory are presented, as well as the literature that is disseminated and scattered in several papers of pioneering researchers who developed the functional analytic framework of this field over the past few decades. Several examples of applications relating to initial and boundary value problems are discussed in detail. The book is intended to advanced graduate researchers and instructors active in research areas with interests in topological properties of fixed point mappings and applications; it also aims to provide students with the necessary understanding of the subject with no deep background material needed. This monograph fills the vacuum in the literature regarding the topological structure of fixed point sets and its applications.
Differential equations. --- Differential inclusions. --- Inclusions, Differential --- Differentiable dynamical systems --- Differential equations --- Set-valued maps --- 517.91 Differential equations --- Differential Equation. --- Differential Inclusion. --- Fixed Point Sets. --- Functional Differential Inclusions. --- Impulsive Differential Equation. --- Impulsive Differential Inclusion. --- Impulsive Semilinear Differential Equation. --- Impulsive Semilinear Differential Inclusion. --- Mild Solution. --- Semigroup. --- Solution Set.
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Impulsive differential equations --- Differential inclusions
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