Fixed points and topological degree in nonlinear analysis
Author(s)
Bibliographic Information
Fixed points and topological degree in nonlinear analysis
（Mathematical surveys, no. 11）
American Mathematical Society, 1964
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Hokkaido University, Library, Graduate School of Science, Faculty of Science and School of Science研究室
DC16:513.8/C8810024157832
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Note
Bibliography: p. 186-193
Description and Table of Contents
Description
The topological methods based on fixed-point theory and on local topological degree which have been developed by Leray, Schauder, Nirenberg, Cesari and others for the study of nonlinear differential equations are here described in detail, beginning with elementary considerations. The reader is not assumed to have any knowledge of topology beyond the theory of point sets in Euclidean n-space which ordinarily forms part of a course in advanced calculus. The methods are first developed for Euclidean n-space and applied to the study of existence and stability of periodic and almost-periodic solutions of systems of ordinary differential equations, both quasi-linear and with 'large' nonlinearities. Then, after being extended to infinite-dimensional 'function-spaces', these methods are applied to integral equations, partial differential equations and further problems concerning periodic solutions of ordinary differential equations.
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