Topological methods, variational methods and their applications : ICM 2002 Satellite Conference on Nonlinear Functional Analysis, Taiyuan, Shan Xi, P.R. China, August 14 - 18, 2002

286 Pages·2003·33.514 MB·English

by  Brezis H., Chang K.C., Li S.J., Rabinowitz P. (eds.)

TopoLoqicAl METkods,
VARiArioNAl METkods
ANd THEIR ApplicATJONS
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ICM 2002 Satellite Conference on
Nonlinear Functional Analysis
TopoloqicAl MeThods,
VARJATJONAI MET hods
ANd rheiR ApplicArioNS
TAiyuAN, ShAN Xi, P.R.ChiNA / Auqusr 14-18, 2002
edited by
H. Brezis
University of Paris VI, France and Rutgers University, USA
K. C. Chang
Peking University, P.R.China
S. J. Li
Chinese Academy of Science, P. R. China
P. Rabinowitz
University of Wisconsin,USA
World Scientific
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British Library Cataloguing-in-Publication Data
A catalogue record for this book is available from the British Library.
TOPOLOGICAL METHODS, VARIATIONAL METHODS AND THEIR
APPLICATIONS
Proceedings of the ICM2002 Satellite Conference on Nonlinear Functional Analysis
Copyright © 2003 by World Scientific Publishing Co. Pte. Ltd.
All rights reserved. This book, or parts thereof, may not be reproduced in any form or by any means,
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ISBN 981-238-262-3
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Preface
ICM 2002 Satellite Conference on Nonlinear Analysis was held in the period:
August 14-18, 2002 at Taiyuan, Shanxi Province, China. This conference was orga-
nized by Mathematical school of Peking University, Academy of Mathematics and
System Sciences of Chinese Academy of Sciences, Mathematical school of Nankai
University, and Department of Mathematics of Shanxi University, and was spon-
sored by Shanxi Province Education Committee, Tian Yuan Mathematics Founda-
tion, and the Shanxi University.
166 mathematicians from 21 countries and areas in the world attended the
conference. 53 invited speakers and 30 contributors presented their lectures. This
conference aims at an overview of the recent development in nonlinear analysis. It
covers the following topics: variational methods, topological methods, fixed point
theory, bifurcations, nonlinear spectral theory, nonlinear Schrodinger equations,
semilinear elliptic equations, Hamiltonian systems, central configuraton in N-body
problems and variational problems arising in geometry and physics.
Many young scholars and graduate students from different universities and
institutes in China joined the conference. The lectures presented in the conference
reflect from different angles the broad and rapid development of nonlinear analysis.
This volume contains most of these lectures.
We wish to thank all the following institutions: Shanxi Province, Shanxi Prov-
ince Education Committee, Shanxi University, National Natural Science Founda-
tion of China and Tien Yuan Math Foundation, for their generous financial support
which made the conference possible, and all the related personnel in Shanxi who
greatly contributed to the success of the conference.
We extend our thanks to all speakers of the conference and the World Scientific
Publisher, specially the editor Dr. Q. Ye , who greatly helped us on the publication
of this proceedings volume.
Hai'm Brezis
Kung-Ching Chang
Shujie Li
Paul H. Rabinowitz
November 2002
v
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Contents
Preface v
List of Academic Committees ix
List of Organizing Committees ix
List of Invited Speakers xi
On the multiplicity of sign changing solutions to nonlinear periodic
Schrodinger equations 1
N. Ackermann
The underlying geometry of the fixed centers problems 11
A. Albany
Nonlinear spectral theory and applications: some current issues 23
J. Appell
Critical equations for the polyharmonic operator 35
T. Bartsch
Standing wave solutions with a critical frequency for nonlinear
Schrodinger equations 45
J. Byeon and Z. Q. Wang
Infinitely many positive energy solutions for semilinear elliptic
equations with concave and convex nonlinearity 53
DM. Cao and P.O. Han
Heat method in nonlinear elliptic equations 65
K.-C. Chang
Some facts and more questions about the Eight 77
A. Chenciner
Boundary blow-up solutions and their applications 89
Y.H. DU
On periodic solutions for forced Van der Pol type equations 99
C. Egami and N. Hirano
A nonlinear Lyapunov-Schmidt reduction and multiple solutions
for some elliptic problem 107
P. Esposito and G. Mancini
p(x}— Laplacian equations 117
X.-L. Fan
Morse theory for strongly indefinite functional and its applications 125
Y.X. Guo
vii
viii
On stability estimates for the regularity property of maps 133
A.D. loffe
Fixed points of increasing operator 143
F. Y. Li
Localized critical points in Banach spaces and sign changing solutions
of nonlinear p-Laplacian equations 151
Z.L. Liu
Collinear central configurations in celestial mechanics 159
Y.M. Long and S.Z. Sun
A maximum principle for bounded solutions of the telegraph equation
and the upper and lower solution method 167
J. Mawhin, R. Ortega and A.M. Robles-Perez
Periodic solutions of nonlinear problems with holomorphic type
of the nonlinearity 175
W. Marzantowicz
Blow-up of quasilinear parabolic equations in Rn — A unified approach .. 185
Y.W. Qi
Remarks on a priori estimates for superlinear elliptic problems 193
M. Ramos
Asymptotics for some nonlinear elliptic systems in Maxwell-Chern-Simons
vortex theory 201
T. Ricciardi
Multi-parameter bifurcation and applications 211
J.P. Shi
field
A semilinear Schrodinger equation with magnetic field 223
A. Szulkin
An exact multiplicity theorem of a P-Laplacian Dirichlet problem
and its application 231
S.-H. Wang and T.-S. Yeh
Symmetry and weighted Sobolev inequalities 241
Z.-Q. Wang
Sign changing solutions of superlinear Schrodinger equations 249
T. Weth
Nonplanar periodic solutions with a fixed energy for Newtonian-like
N > 4-body problems in Rk(k > 3) 259
S.Q. Zhang and Q. Zhou
Existence of positive periodic solution for an impulsive delay
differential equation 269
A. Zhao, W. Yan and J. Yan
Computational theory and methods for finding multiple critical points ... 277
J.X. Zhou
List of Academic Committees
Honorary Chairman:
F. Browder V. Lakshmikantham Tian Fangzeng
Peng Kunchi Guo Guichun
Chairman:
K. C. Chang H. Brezis P. Rabinowitz
Members of Committee:
J. Ma whin Chen Wenyuan
Guo Dajun Liang Zhandong
List of Organizing Committees
Honorary Chairman:
Wang Xin Xiang Congzhi
Liu Diansheng Jia Suotang
Chairman:
Li Shujie Long Yiming Li Shengjia
Members of Committee:
Zhang Shisheng Yan Jurang Wu Xian Li Yongqing
Zhao Lizhu Su Jiabao Zhang Zhitao Zhong Chengkui
Organizer
School of Mathematical Sciences, Peking University
Academy of Mathematics and System Sciences, Chinese Academy of Sciences
College of Mathematics, Nankai University
Department of Mathematics, Shanxi University
ix
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