Uniqueness of the ground state solutions of quasilinear Schr??dinger equations, Nonlinear Analysis: Theory, Methods & Applications, vol.75, issue.2, pp.819-833, 2012. ,
DOI : 10.1016/j.na.2011.09.015
Sobolev spaces, 1975. ,
Bound states of nonlinear Schr??dinger equations with potentials vanishing at infinity, Journal d'Analyse Math??matique, vol.43, issue.1, pp.317-348, 2006. ,
DOI : 10.1007/BF02790279
MULTIPLE BOUND STATES FOR THE SCHR??DINGER???POISSON PROBLEM, Communications in Contemporary Mathematics, vol.10, issue.03, pp.391-404, 2008. ,
DOI : 10.1142/S021919970800282X
Positive solutions to a class of quasilinear elliptic equations on R, Disc, Cont. Dyna. Syst, vol.9, pp.55-68, 2003. ,
On the Schr??dinger???Maxwell equations under the effect of a general nonlinear term, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.27, issue.2, pp.779-791, 2010. ,
DOI : 10.1016/j.anihpc.2009.11.012
Multiple critical points for a class of nonlinear functionals, Annali di Matematica Pura ed Applicata, vol.346, issue.3, pp.507-523, 2011. ,
DOI : 10.1007/s10231-010-0160-3
Ground state solutions for the nonlinear Schr??dinger???Maxwell equations, Journal of Mathematical Analysis and Applications, vol.345, issue.1, pp.90-108, 2008. ,
DOI : 10.1016/j.jmaa.2008.03.057
Mean field dynamics of fermions and??the??time-dependent??Hartree???Fock equation, Journal de Math??matiques Pures et Appliqu??es, vol.82, issue.6, pp.665-683, 2003. ,
DOI : 10.1016/S0021-7824(03)00023-0
Infinitely many solutions of a symmetric Dirichlet problem, Nonlinear Analysis: Theory, Methods & Applications, vol.20, issue.10, pp.1205-1216, 1993. ,
DOI : 10.1016/0362-546X(93)90151-H
Normalized solutions of nonlinear Schr??dinger equations, Archiv der Mathematik, vol.28, issue.1, pp.75-83, 2013. ,
DOI : 10.1007/s00013-012-0468-x
Nonlinear electromagnetic-spin waves, Physics Reports, vol.189, issue.4, pp.165-223, 1990. ,
DOI : 10.1016/0370-1573(90)90093-H
Stable standing waves for a class of nonlinear Schr??dinger-Poisson equations, Zeitschrift f??r angewandte Mathematik und Physik, vol.346, issue.3, pp.267-280, 2011. ,
DOI : 10.1007/s00033-010-0092-1
Scaling properties of functionals and existence of constrained minimizers, Journal of Functional Analysis, vol.261, issue.9, pp.2486-2507, 2011. ,
DOI : 10.1016/j.jfa.2011.06.014
Existence and instability of standing waves with prescribed norm for a class of Schrödinger-Poisson equations, Proc. London Math. Soc. (3), pp.303-339, 2013. ,
An eigenvalue problem for the Schr??dinger-Maxwell equations, Topological Methods in Nonlinear Analysis, vol.11, issue.2, pp.283-293, 1998. ,
DOI : 10.12775/TMNA.1998.019
Instabilité des états stationnaires dans les équations de Schrödinger et de Klein-Gordon non linéaire, C. R. Acad. Sci. Paris Sér. I Math, vol.293, issue.9, pp.489-492, 1981. ,
Nonlinear scalar field equations, I existence of a ground state, Archive for Rational Mechanics and Analysis, vol.82, issue.4, pp.313-346, 1983. ,
DOI : 10.1007/BF00250555
Nonlinear scalar field equations, II existence of infinitely many solutions, Archive for Rational Mechanics and Analysis, vol.82, issue.4, pp.347-375, 1983. ,
DOI : 10.1007/BF00250556
On an Exchange Interaction Model for Quantum Transport: The Schr??dinger???Poisson???Slater System, Mathematical Models and Methods in Applied Sciences, vol.13, issue.10, pp.1185-1217, 2003. ,
DOI : 10.1142/S0218202503002969
Dynamical modulation of an ultrashort high-intensity laser pulse in matter, JETP, vol.77, pp.562-573, 1993. ,
Analyse fonctionnelle, Théorie et applications, Collection Mathématiques Appliquées pour la Maîtrise, 1983. ,
A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer, pp.486-490, 1983. ,
Kato's inequality when ??u is a measure, Comptes Rendus Mathematique, vol.338, issue.8, pp.599-604, 2004. ,
DOI : 10.1016/j.crma.2003.12.032
Solitons on nanotubes and fullerenes as solutions of a modified nonlinear Schrödinger equation Advances in Soliton Research, pp.135-151, 2006. ,
Spinning solitons of a modified nonlinear Schr??dinger equation, Physical Review D, vol.69, issue.8, p.87701, 2004. ,
DOI : 10.1103/PhysRevD.69.087701
Electron self-trapping in a discrete two-dimensional lattice, Physica D: Nonlinear Phenomena, vol.159, issue.1-2, pp.71-90, 2001. ,
DOI : 10.1016/S0167-2789(01)00332-3
-dimensional modified nonlinear Schr??dinger equation, Nonlinearity, vol.16, issue.4, pp.1481-1497, 2003. ,
DOI : 10.1088/0951-7715/16/4/317
Symmetry and monotonicity of least energy solutions, Calculus of Variations and Partial Differential Equations, vol.148, issue.4, pp.481-492, 2009. ,
DOI : 10.1007/s00526-009-0238-1
Fixed point free involutions and equivariant maps. II, Transactions of the American Mathematical Society, vol.105, issue.2, pp.222-228 ,
DOI : 10.1090/S0002-9947-1962-0143208-6
URL : http://projecteuclid.org/download/pdf_1/euclid.bams/1183523747
On a bifurcation value related to quasi-linear Schr??dinger equations, Journal of Fixed Point Theory and Applications, vol.12, issue.1-2, pp.121-133, 2012. ,
DOI : 10.1007/s11784-012-0088-x
EXISTENCE OF STEADY STATES FOR THE MAXWELL???SCHR??DINGER???POISSON SYSTEM: EXPLORING THE APPLICABILITY OF THE CONCENTRATION???COMPACTNESS PRINCIPLE, Mathematical Models and Methods in Applied Sciences, vol.23, issue.10, pp.1915-1938, 2013. ,
DOI : 10.1142/S0218202513500541
A ecessary and Sufficient Condition for The Stability of General molecular Systems, Communications in Partial Differential Equations, vol.17, issue.7, pp.1051-1110, 1992. ,
DOI : 10.1080/03605309208820878
Orbital stability of standing waves for some nonlinear Schr???dinger equations, Communications in Mathematical Physics, vol.49, issue.4, pp.549-561, 1982. ,
DOI : 10.1007/BF01403504
Semilinear Schrödinger equations, Courant Lecture Notes in mathematics 10, 2003. ,
Stability of standing waves for a class of quasilinear Schr??dinger equations, European Journal of Applied Mathematics, vol.6, issue.05, pp.611-633, 2012. ,
DOI : 10.1016/j.apm.2009.03.003
Orbital stability of standing waves of a class of fractional Schrödinger equations with a general Hartreetype integrand, 2013. ,
Solutions for a quasilinear Schr??dinger equation: a dual approach, Nonlinear Analysis: Theory, Methods & Applications, vol.56, issue.2, pp.213-226, 2004. ,
DOI : 10.1016/j.na.2003.09.008
Stability and instability results for standing waves of quasi-linear Schr??dinger equations, Nonlinearity, vol.23, issue.6, pp.1353-1385, 2010. ,
DOI : 10.1088/0951-7715/23/6/006
Existence and multiplicity of positive solutions for the nonlinear Schr??dinger???Poisson equations, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.143, issue.04, pp.745-764, 2013. ,
DOI : 10.1017/S0308210511000692
Solitary waves for nonlinear Klein???Gordon???Maxwell and Schr??dinger???Maxwell equations, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.134, issue.05, pp.893-906, 2004. ,
DOI : 10.1017/S030821050000353X
Non-existence results for the coupled Klein-Gordon-Maxwell equations, Adv. Nonlinear Stud, vol.4, pp.307-322, 2004. ,
Non-radially symmetric solutions of nonlinear Schrödinger equation coupled with Maxwell equations, Adv. Nonlinear Stud, vol.2, pp.177-192, 2002. ,
Global Existence of Small Solutions to a Relativistic Nonlinear Schr??dinger Equation, Communications in Mathematical Physics, vol.189, issue.1, pp.73-105, 1997. ,
DOI : 10.1007/s002200050191
Scattering for the focusing energy-subcritical NLS, Sci, Chima Math, vol.54, pp.2037-2062, 2011. ,
Stability of coulomb systems with magnetic fields, Communications in Mathematical Physics, vol.45, issue.2, pp.251-270, 1986. ,
DOI : 10.1007/BF01211593
Multiple solutions for a quasilinear Schr??dinger equation, Journal of Differential Equations, vol.254, issue.4, pp.2015-2032, 2012. ,
DOI : 10.1016/j.jde.2012.11.017
Exponential decay of solutions to nonlinear elliptic equations with potentials, Zeitschrift f??r angewandte Mathematik und Physik, vol.56, issue.6, pp.1000-1011, 2005. ,
DOI : 10.1007/s00033-005-4060-0
On the radiality of constrained minimizers to the Schr??dinger???Poisson???Slater energy, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.29, issue.3, pp.369-376, 2012. ,
DOI : 10.1016/j.anihpc.2011.12.001
Duality and Perturbation Methods in Critial Point Theory, Cambridge Tracts in Mathematics, vol.107, 1993. ,
Uniqueness of ground states for a class of quasi-linear ellptic equations, Adv. Nonlinear Anal, vol.1, pp.159-179, 2012. ,
Upper hybrid solitons ans oscillating two-stream instabilities, Physics of fuids, vol.19, pp.872-881, 1976. ,
On the variational approach to the stability of standing waves for the nonlinear Schrödinger equation, Adv. Nonlinear Stud, vol.4, issue.4, pp.469-501, 2004. ,
Electrons on hexagonal lattices and applications to nanotubes, Physical Review B, vol.68, issue.18, pp.184-302, 2003. ,
DOI : 10.1103/PhysRevB.68.184302
A general method for the solution of nonlinear soliton and kink Schr???dinger equations, Zeitschrift f???r Physik B Condensed Matter and Quanta, vol.85, issue.1, pp.83-87, 1980. ,
DOI : 10.1007/BF01325508
Nonlinear scalar field equations in R N : mountain pass ans symmetric moutain pass approaches, Top. Meth. Nonlin. Anal, vol.35, pp.253-276, 2010. ,
On blow-up solutions to the 3D cubic Nonlinear Schrödinger Equation, App. Math. Res. Express. AMRX, 2007. ,
Existence of Prescribed-Norm Solutions for a Class of Schrödinger-Poisson Equation, Abstract and Applied Analysis ,
Sign-changing radial solutions for the Schrödinger-Poisson-Slater problem, Topol. Methods Nonlinear Anal, vol.41, issue.2, pp.365-385, 2013. ,
Ground and bound states for a static Schrödinger-Poisson-Slater problem, Comm. Comp. Math, vol.14, issue.1, pp.10-1142, 2012. ,
Existence of solutions with prescribed norm for semilinear elliptic equations, Nonlinear Analysis: Theory, Methods & Applications, vol.28, issue.10, pp.1633-1659, 1997. ,
DOI : 10.1016/S0362-546X(96)00021-1
Sharp nonexistence results of prescribed L 2-norm solutions for some class of Schr??dinger???Poisson and quasi-linear equations, Zeitschrift f??r angewandte Mathematik und Physik, vol.346, issue.1, pp.937-954, 2013. ,
DOI : 10.1007/s00033-012-0272-2
Multiple normalized solutions for quasi-linear Schrödinger equations ,
An approach to minimization under a constraint: the added mass technique, Calculus of Variations and Partial Differential Equations, vol.42, issue.7, pp.3-4, 2011. ,
DOI : 10.1007/s00526-010-0374-7
Stability of standing waves for nonlinear Schrödinger equation with attractive delta potential and repulsive nonlinearity, Saitama Math, J, vol.26, pp.39-48, 2009. ,
Growth properties of solutions of the reduced wave equation with a variable coefficient, Communications on Pure and Applied Mathematics, vol.135, issue.3, pp.403-425, 1959. ,
DOI : 10.1002/cpa.3160120302
On the existence of a solution for elliptic system related to the Maxwell???Schr??dinger equations, Nonlinear Analysis: Theory, Methods & Applications, vol.67, issue.5, pp.1445-1456, 2007. ,
DOI : 10.1016/j.na.2006.07.029
Existence and stability of standing waves for Schrödinger-Poisson-Slater equation, Adv. Nonlinear Stud, vol.7, issue.3, pp.403-437, 2007. ,
Existence and orbital stability of the standing waves for nonlinear Schrödinger equations via the variational method, 2008. ,
Self-Consistent Equations Including Exchange and Correlation Effects, Physical Review, vol.140, issue.4A, pp.1133-1138, 1965. ,
DOI : 10.1103/PhysRev.140.A1133
Large-Amplitude Quasi-Solitons in Superfluid Films, Journal of the Physical Society of Japan, vol.50, issue.10, pp.3262-3267, 1981. ,
DOI : 10.1143/JPSJ.50.3262
Uniqueness of positive solutions of ?u ? u + u p = 0 in R N, Arch. Rational Mech. Anal, vol.105, pp.243-266, 1989. ,
Existence and Uniqueness of the Minimizing Solution of Choquard's Nonlinear Equation, Studies in Applied Mathematics, vol.21, issue.2, pp.93-105, 1977. ,
DOI : 10.1002/sapm197757293
On the lowest eigenvalue of the Laplacian for the intersection of two domains, Invent. math, pp.441-448, 1983. ,
Thomas-Fermi and related theories of atoms and molecules, Rev. Modern Phys, pp.603-641, 1981. ,
The Thomas-Fermi theory of atoms, molecules, and solids, Advances in Math, pp.22-116, 1977. ,
The Chandrasekhar theory of stellar collapse as the limit of quantum mechanics, Communications in Mathematical Physics, vol.187, issue.1, pp.147-174, 1987. ,
DOI : 10.1007/BF01217684
The concentration-compactness principle in the Calculus of Variations. The locally compact case, part 1. * *Mp denotes the Marcinkiewicz space or weak Lp space, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.1, issue.2, pp.109-145, 1984. ,
DOI : 10.1016/S0294-1449(16)30428-0
One dimensional collapse of plasma waves, JETP, Letters, vol.27, pp.517-520, 1978. ,
Quasilinear elliptic equations via perturbation method, Proc. Amer, pp.253-263, 2013. ,
DOI : 10.1090/S0002-9939-2012-11293-6
Soliton solutions for quasilinear Schrödinger equations I, Proc. Amer, pp.441-448, 2003. ,
Soliton solutions for quasilinear Schr??dinger equations, II, Journal of Differential Equations, vol.187, issue.2, pp.473-493, 2003. ,
DOI : 10.1016/S0022-0396(02)00064-5
Solutions for Quasilinear Schr??dinger Equations via the Nehari Method, Communications in Partial Differential Equations, vol.1, issue.2, pp.879-901, 2004. ,
DOI : 10.1007/978-1-4612-4146-1
Multiplicity of normalized solutions for a class of nonlinear Schrödinger- Poisson-Slater equations ,
Non-linear effects in quasi-one-dimensional models of condensed matter theory, Physics Reports, vol.104, issue.1, pp.1-86, 1984. ,
DOI : 10.1016/0370-1573(84)90106-6
The Schr??dinger-Poisson-X?? equation, Applied Mathematics Letters, vol.14, issue.6, pp.759-763, 2001. ,
DOI : 10.1016/S0893-9659(01)80038-0
On universality of blow-up profile for L 2 critical nonlinear Schr???dinger equation, Inventiones Mathematicae, vol.156, issue.3, pp.565-672, 2004. ,
DOI : 10.1007/s00222-003-0346-z
Stable Self-Similar Blow-Up Dynamics for Slightly L 2 Super-Critical Nls Equations, Geometric and Functional Analysis, vol.34, issue.2, pp.1028-1071, 2010. ,
DOI : 10.1007/s00039-010-0081-8
URL : https://hal.archives-ouvertes.fr/hal-00629719
Existence of groundstates for a class of nonlinear Choquard equations, Transactions of the American Mathematical Society, vol.367, issue.9 ,
DOI : 10.1090/S0002-9947-2014-06289-2
On the Local Well Posedness of Quasilinear Schr??dinger Equations in Arbitrary Space Dimension, Journal of Differential Equations, vol.172, issue.1, pp.83-115, 2001. ,
DOI : 10.1006/jdeq.2000.3853
On the existence of soliton solutions to quasilinear Schr??dinger equations, Calculus of Variations and Partial Differential Equations, vol.14, issue.3, pp.329-344, 2002. ,
DOI : 10.1007/s005260100105
Relativistic self-focusing and channel formation in laser-plasma interactions, Physical Review E, vol.50, issue.2, pp.687-689, 1994. ,
DOI : 10.1103/PhysRevE.50.R687
The Schr??dinger???Poisson equation under the effect of a nonlinear local term, Journal of Functional Analysis, vol.237, issue.2, pp.655-674, 2006. ,
DOI : 10.1016/j.jfa.2006.04.005
On the Schr??dinger???Poisson???Slater System: Behavior of Minimizers, Radial and Nonradial Cases, Archive for Rational Mechanics and Analysis, vol.18, issue.5, pp.349-368, 2010. ,
DOI : 10.1007/s00205-010-0299-5
Existence of ground states for a modified nonlinear Schr??dinger equation, Nonlinearity, vol.23, issue.5, pp.1221-1233, 2010. ,
DOI : 10.1088/0951-7715/23/5/011
Long-Time Dynamics of the Schr??dinger???Poisson???Slater System, Journal of Statistical Physics, vol.114, issue.1/2, pp.179-204, 2004. ,
DOI : 10.1023/B:JOSS.0000003109.97208.53
Uniqueness and nondegeneracy of the ground state for a quasilinear Schr??dinger equation with a small parameter, Nonlinear Analysis: Theory, Methods & Applications, vol.74, issue.5, pp.1731-1737, 2011. ,
DOI : 10.1016/j.na.2010.10.045
Multiple positive solutions for a Schr??dinger???Poisson???Slater system, Journal of Mathematical Analysis and Applications, vol.365, issue.1, pp.288-299, 2010. ,
DOI : 10.1016/j.jmaa.2009.10.061
A minimization problem for the Nonlinear Schr??odinger-Poisson type Equation, The S??o Paulo Journal of Mathematical Sciences, vol.5, issue.2, pp.149-173, 2011. ,
DOI : 10.11606/issn.2316-9028.v5i2p149-173
A Simplification of the Hartree-Fock Method, Physical Review, vol.81, issue.3, pp.385-390, 1951. ,
DOI : 10.1103/PhysRev.81.385
Applications to Nonlinear Partial Differential Equations and Hamiltonian Systems, 1996. ,
Positive solution for a nonlinear stationary Schrödinger-Poisson system in R 3 , Discrete Contin, Dyn. Syst, vol.18, issue.4, pp.809-816, 2007. ,
Nonlinear Schr???dinger equations and sharp interpolation estimates, Communications in Mathematical Physics, vol.41, issue.4, pp.567-576, 1983. ,
DOI : 10.1007/BF01208265
Progress in Nonlinear Differential Equations and their Applications, 24, 1996. ,
Existence and stability of standing waves for nonlinear fractional Schrödinger equations with Hartree type nonlinearity, J. Math. Anal. Appl ,
On the existence of solutions for the Schr??dinger???Poisson equations, Journal of Mathematical Analysis and Applications, vol.346, issue.1, pp.155-169, 2008. ,
DOI : 10.1016/j.jmaa.2008.04.053