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 PDF
Preview 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
TopoLoqicAl METkods, VARiArioNAl METkods ANd THEIR ApplicATJONS This page intentionally left blank 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 New Jersey • London • Singapore • Hong Kong Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: Suite 202, 1060 Main Street, River Edge, NJ 07661 UK office: 57 Shelton Street, Covent Garden, London WC2H 9HE 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, electronic or mechanical, including photocopying, recording or any information storage and retrieval system now known or to be invented, without written permission from the Publisher. For photocopying of material in this volume, please pay a copying fee through the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, USA. In this case permission to photocopy is not required from the publisher. ISBN 981-238-262-3 Printed in Singapore by World Scientific Printers (S) Pte Ltd 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 This page intentionally left blank 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 This page intentionally left blank
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