CONTENTS -- Preface -- M/v A. Bahri -- 1. Introduction -- 2. The path spaces, the nearly symmetric -- The nearly symmetric -- 3. M/v -- 3.1. ^c and the fundamental domain -- 3.2. How O1 dominates O3: A special case -- 3.3. The general case -- 3.4. Outline of the construction of M/v -- 4. The functional -- 4.1. Proposition 4.1 -- 4.2. M*/v and the symmetric s -- 4.3. Js near the hyperbolic orbits -- 4.4. Three additional observations -- References -- Nonlinear elliptic equations of in nite order A. Benkirane, M. Chrif, and S. El Manouni -- 1. Introduction -- 2. Preliminaries -- 3. Main result -- 4. Concluding remarks -- Acknowledgments -- References -- Some remarks on a sign condition for perturbations of nonlinear problems A. Benkirane, J. Benouna, and M. Rhoudaf -- 1. Introduction -- 2. Main results -- References -- On the principle eigencurve of a coupled system A. El Khalil -- 1. Introduction -- 2. Preliminaries -- 2.1. Functional framework -- 2.2. Definitions -- 2.3. Auxiliary lemmas -- 3. Main results -- References -- Parabolic inclusions with nonlocal conditions A. Boucherif -- 1. Introduction -- 2. Preliminaries -- 3. Linear nonhomogeneous problem -- 4. Multivalued functions -- 5. Main results -- 5.1. Lipschitz multivalued right-hand sides -- 5.2. Upper semicontinuous right-hand sides -- 5.3. Lower semicontinuous right-hand sides -- 5.4. Method of lower and upper solutions -- References -- Periodic solutions of nonlinear parabolic equations with measure data and polynomial growth in jruj A. El Hachimi and A. Lamrani Alaoui -- 1. Introduction -- 2. Necessary conditions for existence -- 3. Existence in the case of natural growth and regular measure data -- 3.1. Some known results -- 3.2. Definition and main result -- 3.3. Regularization and existence of approximate solutions -- 3.4. A priori estimates and passage to the limit -- References.

Existence and L1-regularity results for some nonlinear elliptic Dirichlet problems A. Youss -- 1. Introduction -- 2. Standard growth -- 3. Nonstandard growth -- References -- Analysis of a new mixed formulation of the obstacle problem B. Seddoug, A. Addou, and A. Lidouh -- 1. Introduction -- 2. Survey of the abstract problem -- 2.1. The continuous problem -- 2.2. Reformulation of the problem -- 2.3. Property of stability -- 2.4. The discrete problem -- 3. Study of an obstacle problem -- 3.1. The continuous problem -- 3.2. The discrete problem -- 3.3. Some numerical results -- Current and future developments -- Acknowledgement -- References -- An obstacle problem via a sequence of penalized problems E. Azroul and M. Rhoudaf -- 1. Introduction -- 2. Preliminaries and basic assumptions -- 3. Some technical lemmas -- 3.1. Some functional properties of time-regularization of a function u -- 3.2. Some weighted imbedding and compactness results -- 3.3. Main results -- References -- Numerical analysis of slopes stability under seismic loading in Lebanon F. Hage Chehade and M. Sadek -- 1. Introduction -- 2. Dynamic analysis -- 2.1. Problem under consideration and basic equations -- 2.2. Elastic response -- 2.3. Inuence of plasticity -- 3. Conclusion -- References -- Existence and uniqueness result for a class of nonlinear parabolic equations with L1 data H. Redwane -- 1. Introduction -- 2. Assumptions on the data and definition of a renormalized solution -- 3. Existence result -- 4. Comparison principle and uniqueness result -- References -- Existence and uniqueness of solutions of some nonlinear equations in Orlicz spaces and weighted Sobolev spaces L. Aharouch, A. Benkirane, J. Bennouna, and A. Touzani -- 1. Definition and existence of renormalized solutions in Orlicz space -- 2. Definition and existence of entropy solutions in Orlicz space.

3. Existence and uniqueness of solution of unilateral problems with L1-data in Orlicz spaces -- 4. Existence of solutions for nonlinear elliptic degenerated equations -- 4.1. Regularity and existence of weak solutions -- 4.2. Existence of renormalized solutions -- References -- Existence of solutions for variational degenerated unilateral problems L. Aharouch, E. Azroul, and M. Rhoudaf -- 1. Introduction -- 2. Preliminaries -- 3. Main results -- 4. Proof of Theorem 3.1 -- 5. Appendix -- References -- Existence and multiplicity results for some p(x)-Laplacian Neumann problems M. Bendahmane, M. Chrif, and S. El Manouni -- 1. Introduction -- 2. Preliminaries -- 3. Proof of the main result -- Acknowledgement -- References -- Positive solutions with changing sign energy to nonhomogeneous elliptic problem of fourth order M. Talbi and N. Tsouli -- 1. Introduction -- 2. Preliminary results -- 3. Existence results -- References -- A survey on potential theory on Orlicz spaces N. A ssaoui -- 1. Introduction -- 2. Preliminaries -- 2.1. Orlicz spaces -- 2.2. Capacity and Bessel potentials -- 3. Capacity and non linear potential in Orlicz spaces -- 4. On the Bessel potentials in Orlicz spaces -- 4.1. On the continuity of Bessel potentials in Orlicz spaces -- 4.2. Instability of capacity in Orlicz spaces -- 4.3. Bessel potentials in Orlicz spaces -- 5. Another developments of strongly nonlinear potential theory -- 5.1. Maximal operators and potentials -- 5.2. Quasicontinuity -- 5.3. Operations on potentials, Other definition of capacity and removable singularities -- 6. Capacitary type estimates in strongly nonlinear potential theory and applications -- 6.1. A capacitary type estimate -- 6.2. A space of quasicontinuous functions -- 6.3. Maximal operators and capacity.

7. Maximal operators, Lebesgue points and quasicontinuity in strongly nonlinear potential theory -- 8. Wolff inequality in strongly nonlinear potential theory and applications -- 8.1. A Wolff type inequality -- 8.2. Capacity and Hausdorff measure -- 8.3. Lipschitz mappings and capacities -- 9. On the A-Laplacian -- 9.1. A non resolvability result -- 9.2. A resolvability result -- References -- Back on stochastic model for sandpile N. Igbida -- 1. Introduction -- 2. The stochastic model for sandpile problem (cf.6) -- 3. Main results -- Acknowledgements -- References -- On radial solutions for Navier boundary eigenvalue problem with p-biharmonic operator S. El Habib and N. Tsouli -- 1. Introduction -- 2. Preliminaries -- 3. Existence of radial solutions -- 4. Zeros points of eigenfunctions -- 5. Main result -- References -- Floquet states of periodically time-dependent harmonic oscillators Y. Achkar, S. Sayouri, and A. L. Marrakchi -- 1. Introduction -- 2. Formalism -- 2.1. Floquet approach -- 2.2. Jump operators -- 2.3. Resonating averages method (RAM) -- 2.3.1. First order and first order ameliorated solutions -- 2.3.2. Second order and second order ameliorated solutions -- 3. Applications -- 3.1. Forced harmonic oscillator (FHO) -- 3.1.1. First order calculations -- 3.1.2. Second order calculations -- 3.1.3. Jump operators -- 3.1.4. Comparisons and discussions -- 3.2. Pulsating Harmonic Oscillator -- 3.2.1. First order solutions -- 3.2.2. Second order solutions -- 3.3. Harmonic oscillator with a periodical frequency -- 3.3.1. First order Floquet operators and Floquet states -- 3.3.2. Second order Floquet operators and Floquet states -- 3.4. Harmonic Oscillator with time-dependent mass and frequency -- 3.4.1. First order solutions -- 3.4.2. Second order solutions -- 4. Conclusion -- References.

Renormalized solutions of nonlinear degenerated parabolic problems: Existence and uniqueness Y. Akdim, J. Bennouna, M. Mekkour, and M. Rhoudaf -- 1. Introduction -- 2. Preliminaries and basic assumptions -- 3. Main results -- References -- Solvability of quasilinear degenerated elliptic equations with L1 data Y. Akdim -- 1. Introduction -- 2. Preliminaries -- 3. Main result -- 3.1. Example -- References -- Combined fuzzy sliding mode controller for a class of nonlinear systems Y. Alaoui Ha di, J. Boumhidi, and I. Boumhidi -- 1. Introduction -- 2. Problem formulation -- 3. Fuzzy sliding mode control design -- 4. Simulation results -- 5. Conclusion -- References -- Author Index.