Ammari H., Benkirane A., Touzani A. (editors) Recent Developments in Nonlinear Analysis
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RECENT
DEVELOPMENTS
IN NONLINEAR
ANALYSIS
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NEW JERSEY
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LONDON
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SINGAPORE
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BEIJING
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SHANGHAI
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HONG KONG
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TAIPEI
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CHENNAI
World Scientific
editors
Habib Ammari
École Polytechnique, France
Abdelmoujib Benkirane
Faculty of Sciences of Fez, Morocco
Abdelfettah Touzani
Faculty of Sciences of Fez, Morocco
RECENT
DEVELOPMENTS
IN NONLINEAR
ANALYSIS
Proceedings of the Conference in
Mathematics and Mathematical Physics
Fez, Morocco 28 – 30 October 2008
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ISBN-13 978-981-4295-56-7
ISBN-10 981-4295-56-6
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RECENT DEVELOPMENTS IN NONLINEAR ANALYSIS
Proceedings of the Conference in Mathematics and Mathematical Physics
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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 theo-
retical 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 ex-
citing 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 Ecole Polytechnique, France
A. Benkirane and A. Touzani Faculty of Sciences of Fez, Morocco
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CONTENTS
Preface v
M/v 1
A. Bahri
Nonlinear elliptic equations of infinite order 17
A. Benkirane, M. Chrif, and S. El Manouni
Some remarks on a sign condition for perturbations of non-
linear problems 30
A. Benkirane, J. Benouna, and M. Rhoudaf
On the principle eigencurve of a coupled system 43
A. El Khalil
Parabolic inclusions with nonlocal conditions 54
A. Boucherif
Periodic solutions of nonlinear parabolic equations with mea-
sure data and polynomial growth in |∇u| 72
A. El Hachimi and A. Lamrani Alaoui
Existence and L
∞
-regularity results for some nonlinear ellip-
tic Dirichlet problems 88
A. Youssfi
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Analysis of a new mixed formulation of the obstacle problem 101
B. Seddoug, A. Addou, and A. Lidouh
An obstacle problem via a sequence of penalized problems 123
E. Azroul and M. Rhoudaf
Numerical analysis of slopes stability under seismic loading
in Lebanon 141
F. Hage Chehade and M. Sadek
Existence and uniqueness result for a class of nonlinear
parabolic equations with L
1
data 150
H. Redwane
Existence and uniqueness of solutions of some nonlinear equa-
tions in Orlicz spaces and weighted Sobolev spaces 170
L. Aharouch, A. Benkirane, J. Bennouna, and A. Touzani
Existence of solutions for variational degenerated unilateral problems 181
L. Aharouch, E. Azroul, and M. Rhoudaf
Existence and multiplicity results for some p(x)-Laplacian
Neumann problems 205
M. Bendahmane, M. Chrif, and S. El Manouni
Positive solutions with changing sign energy to nonhomoge-
neous elliptic problem of fourth order 217
M. Talbi and N. Tsouli
A survey on potential theory on Orlicz spaces 234
N. A¨ıssaoui
Back on stochastic model for sandpile 266
N. Igbida
On radial solutions for Navier boundary eigenvalue problem
with p-biharmonic operator 278
S. El Habib and N. Tsouli
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Floquet states of periodically time-dependent harmonic oscillators 290
Y. Achkar, S. Sayouri, and A. L. Marrakchi
Renormalized solutions of nonlinear degenerated parabolic
problems: Existence and uniqueness 327
Y. Akdim, J. Bennouna, M. Mekkour, and M. Rhoudaf
Solvability of quasilinear degenerated elliptic equations with
L
1
data 344
Y. Akdim
Combined fuzzy sliding mode controller for a class of nonlin-
ear systems 355
Y. Alaoui Hafidi, J. Boumhidi, and I. Boumhidi
Author Index 365