Topological Fixed Point Principles for Boundary Value Problems

Jan Andres, Lech Gorniewicz - Collection Topological Fixed Point Theory and Its Applications

762 pages, parution le 31/07/2003

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Résumé

The book is devoted to the topological fixed point theory both for single-valued and multivalued mappings in locally convex spaces, including its application to boundary value problems for ordinary differential equations (inclusions) and to (multivalued) dynamical systems. It is the first monograph dealing with the topological fixed point theory in non-metric spaces. Although the theoretical material was tendentiously selected with respect to applications, the text is self-contained. Therefore, three appendices concerning almost-periodic and derivo-periodic single-valued (multivalued) functions and (multivalued) fractals are supplied to the main three chapters.

In Chapter I, the topological and analytical background is built. Then, in Chapter II, topological principles necessary for applications are developed. Finally, in Chapter III, boundary value problems for differential equations and inclusions are investigated in detail by means of the results in Chapter II.

This monograph will be especially useful for post-graduade students and researchers interested in topological methods in nonlinear analysis, particularly in differential equations, differential inclusions and (multivalued) dynamical systems. The content is also likely to stimulate the interest of mathematical economists, population dynamics experts as well as theoretical physicists exploring the topological dynamics.

Written for: Post-graduade students and researchers; mathematical economists, population dynamics experts; theoretical physicists

Sommaire

Theoretical Background
- Structure of locally convex spaces
- ANR-spaces and AR-spaces
- Multivalued mappings and their selections
- Admissible mappings
- Special classes of admissible mappings
- Lefschetz fixed point theorem for admissible mappings
- Lefschetz fixed point theorem for condensing mappings
- Fixed point index and topological degree for admissible maps in locally convex spaces
- Noncompact case
- Nielsen number
- Nielsen number: Noncompact case
- Remarks and comments
General Principles
- Topological structure of fixed point sets: Aronszajn Browder Gupta-type results
- Topological structure of fixed point sets: inverse limit method
- Topological dimension of fixed point sets
- Topological essentiality
- Relative theories of Lefschetz and Nielsen
- Periodic point principles
- Fixed point index for condensing maps
- Approximation method for the fixed point theory of multivalued mappings
- Topological degree defined by means of approximation methods
- Continuation principles based on a fixed point index
- Continuation principles based on a coincidence index
- Remarks and comments
Application to Differential Equations and Inclusions
- Topological approach to differential equations and inclusions
- Topological structure of solution sets: initial value problems
- Topological structure of solution sets: boundary value problems
- Poincaré operators
- Existence results
- Multiplicity results
- Wazewski-type results
- Bounding and guiding functions approach
- Infinitely many subharmonics
- Almost-periodic problems
- Some further applications
- Remarks and comments
Appendices
- Almost-periodic single-valued and multivalued functions
- Derivo-periodic single-valued and multivalued functions
- Fractals and multivalued fractals

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	PAPIER
Éditeur(s)	Kluwer Academic Publishers
Auteur(s)	Jan Andres, Lech Gorniewicz
Collection	Topological Fixed Point Theory and Its Applications
Parution	31/07/2003
Nb. de pages	762
Format	16,5 x 24,5
Couverture	Broché
Poids	1500g
Intérieur	Noir et Blanc
EAN13	9781402013805
ISBN13	978-1-4020-1380-5