| Softcover ISBN: | 978-0-8218-1511-3 |
| Product Code: | SURV/11 |
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| eBook ISBN: | 978-1-4704-1239-5 |
| Product Code: | SURV/11.E |
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| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-0-8218-1511-3 |
| eBook: ISBN: | 978-1-4704-1239-5 |
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| AMS Member Price: | $203.20 $153.20 |
| Softcover ISBN: | 978-0-8218-1511-3 |
| Product Code: | SURV/11 |
| List Price: | $129.00 |
| MAA Member Price: | $116.10 |
| AMS Member Price: | $103.20 |
| eBook ISBN: | 978-1-4704-1239-5 |
| Product Code: | SURV/11.E |
| List Price: | $125.00 |
| MAA Member Price: | $112.50 |
| AMS Member Price: | $100.00 |
| Softcover ISBN: | 978-0-8218-1511-3 |
| eBook ISBN: | 978-1-4704-1239-5 |
| Product Code: | SURV/11.B |
| List Price: | $254.00 $191.50 |
| MAA Member Price: | $228.60 $172.35 |
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Book DetailsMathematical Surveys and MonographsVolume: 11; 1964; 198 ppMSC: Primary 34; Secondary 57
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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Table of Contents
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Chapters
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I. Topological techniques in Euclidean $n$-space
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II. Applications to ordinary differential equations
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III. Topological techniques in function space
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IV. Applications to integral equations, partial differential equations and ordinary differential equations with large nonlinearities
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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.
-
Chapters
-
I. Topological techniques in Euclidean $n$-space
-
II. Applications to ordinary differential equations
-
III. Topological techniques in function space
-
IV. Applications to integral equations, partial differential equations and ordinary differential equations with large nonlinearities
