文档介绍：CRITICAL POINT THEORY AND
ITS APPLICATIONS
CRITICAL POINT THEORY AND
ITS APPLICATIONS
By
WENMING ZOU
Tsinghua University, Beijing, China
MARTIN SCHECHTER
University of California, Irvine, California, USA
^ Sprringei r
Library of Congress Control Number: 2006921852
ISBN-10: 0-387-32965-X e-ISBN: 0-387-32968-4
ISBN-13: 978-0-387-32965-9
Printed on acid-free paper.
AMS Subject Classifications: 35J50, 58E05, 47J30, 49505, 58E30
© 2006 Springer Sciencen-Business Media, LLC
All rights reserved. This work may not be translated or copied in whole or in part without the written
permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY
10013, USA), except for brief excerpts in connection with reviews or scholarly analysis. Use in
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or by similar or dissimilar methodology now known or hereafter developed is forbidden.
The use in this publication of trade names, trademarks, service marks, and similar terms, even if they are
not identified as such, is not to be taken as an expression of opinion as to whether or not they are subject
to proprietary rights.
Printed in the United States of America.
987654321
W. Zou dedicates this book to his parents:
LIANG-SHENG ZOU & GUO-XIU ZENG.
M. Schechter dedicates this book to his wife, children and
grandchildren (currently 22) and great grandchildren (currently one).
Contents
Preface ix
1 Preliminaries 1
Partition of Unity in Metric Spaces 1
Sobolev Spaces 2
Differentiable Functionals 7
Topological Degrees 13
An ODE in Banach Space 16
The (PS) Conditions 19
Weak Solutions 20
2 Functionals Bounded Below 25
Pseudo-Gradients 25
Bounded Minimizing Sequences 26
An Application 31
3 Even Functionals 37
Abstract Theorems 37
High Energy Solutions