Coincidence Degree, and Nonlinear Differential Equations
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568 Robert E. Gaines Jean L. Mawhin
Coincidence Degree, and Nonlinear Differential Equations
Springer-Verlag Berlin.Heidelberg • New York 1977
Authors
Robert E. Gaines C o l o r a d o State University Department of Mathematics Fort Collins Colorado 80523/USA
Jean L. Mawhin Universit@ Catholique de Louvain Institut Math@matique B - 1 3 4 8 Louvain-la-Neuve/Belgium
Library of Congress Cataloging in Publication Data
Gaines, Robert E
1941Coincidence degree, and nonlinear differential equations.
(Lecture notes in mathematics ; 568) Includes bibliographical references and index. i. Differential equations~ Nonlinear. 2. Boundary value problems. 5o Coincidence theory (Mathematics) I. Mawhin~ J., joint author. II. Title. III. Series: Lecture notes in mathematics (Berlin)
568.
QA3.L28
no. 568
[QA372]
510'.8s [515'.35] 76-58459
AMS Subject Classifications (1970): 34 B15, 34 K10, 35J 65, 47 H 15, 5 5 C 2 0 ISBN 3-540-08067-8 Springer-Verlag Berlin • Heidelberg • New York ISBN 0-387-08067-8 Springer-Verlag New York • Heidelberg - Berlin This work is subject to copyright. All rights are reserved, whether the whole or part of the material is concerned, specifically those of translation, reprinting, re-use of illustrations, broadcasting, reproduction by photocopying machine or similar means, and storage in data banks. Under § 54 of the German Copyright Law where copies are made for other than private use, a fee is payable to the publisher, the amount of the fee to be determined by agreement with the publisher. © by Springer-Verlag Berlin • Heidelberg 1977 Printed in Germany Printing and binding: Beltz Offsetdruck, Hemsbach/Bergstr. 2141/3140/543210
To Margaret, Marie~ Val@rie~ Jean and
Martha, Laura, Elissa.
TABLE OF CONTENTS I. Introduction II. Alternative III. Coincidence
problems
: an historical
perspective
degree for perturbations
of Fredholm 10
mappings IV. A generalized theorems
continuation
theorem and existence
for Lx = Nx
V. Two-point boundary value problems without
special
VI. Approximation
structure
of solutions
VII. Quasibounded perturbations VIII. Boundary value problems partial differential IX. Periodic
: nonlinearities
differential X. Coincidence
104
of Fredholm mappings
134
for some semilinear
elliptic
equations
151
nonlinearities
equations
and of functional 166
equations index, multiplicity
and bifurcation
theory XI. Coincidence
36
- The projection method
solutions of ordinary differential
with quasibo~nded
26
189
degree for k-set contractive perturbations 209
of linear Fredholm mappings XII. Nonlinear perturbations nonzero index
of Fredholm mappings
of
229
References
242
Index
261
I. INTRODUCTION
This work has its origin in lectures given by J. Mawhin in 1974 at the University of Brasilia and by R.E. Gaines in 1975 at the University of Louvain.
Those lectures respectively covered chapters II to IV, VII to IX
and chapters V-VI.
Chapters X to XII have been added to include more
recent material. The emphasis of the work is on the use of topolog
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