Degree theory in analysis and applications
著者
書誌事項
Degree theory in analysis and applications
（Oxford lecture series in mathematics and its applications, 2）
Clarendon Press, 1995
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注記
Bibliography: p.[205]-208
Includes index
内容説明・目次
内容説明
In this book we study the degree theory and some of its applications in analysis. It focuses on the recent developments of this theory for Sobolev functions, which distinguishes this book from the currently available literature. We begin with a thorough study of topological degree for continuous functions. The contents of the book include: degree theory for continuous functions, the multiplication theorem, Hopf`s theorem, Brower`s fixed point theorem, odd
mappings, Jordan`s separation theorem. Following a brief review of measure theory and Sobolev functions and study local invertibility of Sobolev functions. These results are put to use in the study variational principles in nonlinear elasticity. The Leray-Schauder degree in infinite dimensional spaces is
exploited to obtain fixed point theorems. We end the book by illustrating several applications of the degree in the theories of ordinary differential equations and partial differential equations.
目次
- 1. Degree theory for continuous functions
- 2. Degree theory in finite dimensional spaces
- 3. Some applications of the degree theory to Topology
- 4. Measure theory and Sobolev spaces
- 5. Properties of the degree for Sobolev functions
- 6. Local invertibility of Sobolev functions. Applications
- 7. Degree in infinite dimensional spaces
- References
- Index
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