Fixed Points and Topological Degree in Nonlinear Analysis

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Fixed Points and Topological Degree in Nonlinear Analysis
Categories :"Electronic books"
Author By :"Jane Cronin"
Published Date : 1995-01-05
Published by : American Mathematical Soc.
Books Language : en

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.

The two topological concepts we use are the fixed point theorem and local \u003cbr\u003e\ntopological \u003cb\u003edegree\u003c/b\u003e (hereafter to be termed local \u003cb\u003edegree\u003c/b\u003e or \u003cb\u003edegree\u003c/b\u003e). The fixed \u003cbr\u003e\npoint theorem is couched in simple terms and we will be able to state it with \u003cbr\u003e\npractically no ...

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