Recent Developments In Nonlinear Analysis

RECENT DEVELOPMENTS IN NONLINEAR ANALYSIS 7641 tp.indd 1 1/28/10 2:23:20 PM This page intentionally left blank RECENT DEVELOPMENTS IN NONLINEAR ANALYSIS Proceedings of the Conference in Mathematics and Mathematical Physics Fez, Morocco 28 – 30 October 2008 editors Habib Ammari École Polytechnique, France Abdelmoujib Benkirane Faculty of Sciences of Fez, Morocco Abdelfettah Touzani Faculty of Sciences of Fez, Morocco World Scientific NEW JERSEY 7641 tp.indd 2 • LONDON • SINGAPORE • BEIJING • SHANGHAI • HONG KONG • TA I P E I • CHENNAI 1/28/10 2:23:20 PM Published by World Scientific Publishing Co. Pte. Ltd. 5 Toh Tuck Link, Singapore 596224 USA office: 27 Warren Street, Suite 401-402, Hackensack, NJ 07601 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. RECENT DEVELOPMENTS IN NONLINEAR ANALYSIS Proceedings of the Conference in Mathematics and Mathematical Physics Copyright © 2010 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-13 978-981-4295-56-7 ISBN-10 981-4295-56-6 Printed in Singapore. LaiFun - Recent Development in Nonlinear.pmd1 12/28/2009, 1:28 PM December 28, 2009 12:15 WSPC - Proceedings Trim Size: 9in x 6in recent v PREFACE The Conference of Mathematics and Mathematical Physics was held in Fez, Morocco during the period 28–30 October, 2008. It was part of the 5th Congress of the Scientific Research Outlook and Technology Development in the Arab World. The present volume contains the texts of a selection from among the many interesting presentations delivered at the conference. The main objectives of the conference were to promote exchange of the most recent results and emerging ideas and also to merge expertise of researchers in the field not only from the Arab countries but from around the World. The conference covered in a broad and balanced fashion both the theoretical and applied parts of modern nonlinear analysis. Both the Local Organizing and Programme Committees deserve great thanks in creating a well-run and very productive conference, with an exciting programme of keynote lectures and contributed talks. It is a pleasure to thank all of them for their hard work. The support of the Arab Science and Technology Foundation and its president Dr. Abdalla A. Alnajjar are also gratefully acknowledged. August 6th, 2009 H. Ammari A. Benkirane and A. Touzani Ecole Polytechnique, France Faculty of Sciences of Fez, Morocco December 28, 2009 12:15 WSPC - Proceedings Trim Size: 9in x 6in This page intentionally left blank recent December 28, 2009 12:15 WSPC - Proceedings Trim Size: 9in x 6in recent vii CONTENTS Preface v M/v A. Bahri 1 Nonlinear elliptic equations of infinite order A. Benkirane, M. Chrif, and S. El Manouni Some remarks on a sign condition for perturbations of nonlinear problems A. Benkirane,