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- DescriptionThe 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 nlinear differential equations are here described in detail, beginning with elementary considerations. The reader is t assumed to have any kwledge 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' nlinearities. 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.
- Author(s)Jane Cronin
- PublisherAmerican Mathematical Society
- Date of Publication02/07/1992
- Series TitleMathematical Surveys and Monographs
- Series Part/Volume NumberNo. 11
- Place of PublicationProvidence
- Country of PublicationUnited States
- ImprintAmerican Mathematical Society
- Weight384 g
- Edition Statement5th
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