S. Agmon, Lectures on exponential decay of solutions of second-order elliptic equations: bounds on eigenfunctions of N -body Schrödinger operators, pp.29-34, 1982.
DOI : 10.1515/9781400853076

C. Bonanno, P. Avenia, M. Ghimenti, and M. Squassina, Soliton dynamics for the generalized Choquard equation, Journal of Mathematical Analysis and Applications, vol.417, issue.1, pp.180-199, 2014.
DOI : 10.1016/j.jmaa.2014.02.063

P. Choquard and J. Stubbe, The One-Dimensional Schr??dinger???Newton Equations, Letters in Mathematical Physics, vol.40, issue.19, pp.177-184, 2007.
DOI : 10.1007/s11005-007-0174-y

P. Choquard, J. Stubbe, and M. Vuffray, Stationary solutions of the Schrödinger? Newton model?an ODE approach, Differential Integral Equations, vol.21, issue.78, pp.665-679, 2008.

S. Cingolani, M. Clapp, and S. Secchi, Multiple solutions to a magnetic nonlinear Choquard equation, Zeitschrift f??r angewandte Mathematik und Physik, vol.26, issue.2, pp.233-248, 2012.
DOI : 10.1007/s00033-011-0166-8

S. Cingolani, S. Secchi, and M. Squassina, Abstract, Proceedings of the Royal Society of Edinburgh: Section A Mathematics, vol.140, issue.05, pp.973-1009, 2010.
DOI : 10.1017/S0308210509000584

S. Cingolani and T. Weth, On the planar Schr??dinger???Poisson system, Annales de l'Institut Henri Poincare (C) Non Linear Analysis, vol.33, issue.1, pp.169-197, 2016.
DOI : 10.1016/j.anihpc.2014.09.008

P. D. Avenia and M. Squassina, SOLITON DYNAMICS FOR THE SCHR??DINGER???NEWTON SYSTEM, Mathematical Models and Methods in Applied Sciences, vol.24, issue.03, pp.553-572, 2014.
DOI : 10.1142/S0218202513500590

L. Diósi, Gravitation and quantum-mechanical localization of macro-objects, Physics Letters A, vol.105, issue.4-5, pp.199-202, 1984.
DOI : 10.1016/0375-9601(84)90397-9

H. Genev and G. Venkov, Soliton and blow-up solutions to the time-dependent Schrödinger-Hartree equation, Discrete Contin, Dyn. Syst. Ser. S, vol.5, issue.5, pp.903-923, 2012.

R. Harrison, T. Moroz, and K. P. Tod, A numerical study of the Schr??dinger??Newton equations, Nonlinearity, vol.16, issue.1, pp.101-122, 2003.
DOI : 10.1088/0951-7715/16/1/307

K. R. Jones, Newtonian Quantum Gravity, Australian Journal of Physics, vol.48, issue.6, pp.1055-1081, 1995.
DOI : 10.1071/PH951055

E. Lenzmann, Uniqueness of ground states for pseudorelativistic Hartree equations, Analysis & PDE, vol.2, issue.1, pp.1-27, 2009.
DOI : 10.2140/apde.2009.2.1

E. H. Lieb, Existence and uniqueness of the minimizing solution of Choquard's nonlinear equation, Studies in Appl. Math, vol.5777, issue.2, pp.93-105, 1976.

P. Lions, Solutions of Hartree-Fock equations for Coulomb systems, Communications in Mathematical Physics, vol.22, issue.1, pp.33-97, 1984.
DOI : 10.1007/BF01205672

L. Ma and L. Zhao, Classification of Positive Solitary Solutions of the Nonlinear Choquard Equation, Archive for Rational Mechanics and Analysis, vol.100, issue.109???145, pp.455-467, 2010.
DOI : 10.1007/s00205-008-0208-3

S. Masaki, Energy Solution to a Schr??dinger???Poisson System in the Two-Dimensional Whole Space, SIAM Journal on Mathematical Analysis, vol.43, issue.6, pp.2719-2731, 2011.
DOI : 10.1137/100792019

G. P. Menzala, On the nonexistence of solutions for an elliptic problem in unbounded domains, Funkcial. Ekvac, vol.26, issue.3, pp.231-235, 1983.

V. Moroz and J. Van-schaftingen, Nonlocal Hardy type inequalities with optimal constants and remainder terms ?19 [21] , Groundstates of nonlinear Choquard equations: Existence, qualitative properties and decay asymptotics, Ann. Univ. Buchar. Math. Ser.LXI) J. Funct. Anal, vol.3, issue.265 2 2, pp.187-200, 2012.

R. B. Paris, Incomplete gamma and related functions, NIST Handbook of Mathematical Functions, pp.173-192, 2010.

R. Penrose, On Gravity's role in Quantum State Reduction, General Relativity and Gravitation, vol.44, issue.5, pp.581-600, 1996.
DOI : 10.1007/BF02105068

URL : http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.468.2731

E. M. Stein, G. Weiss, and N. J. , Introduction to Fourier analysis on Euclidean spaces, Princeton Mathematical Series, vol.32, issue.13, pp.4-14, 1971.
DOI : 10.1515/9781400883899

J. Stubbe, Bound states of two-dimensional Schrödinger?Newton equations, available at 0807.4059v1. ?2, 2008.

N. M. Temme, Error functions, Dawson's and Fresnel integrals, NIST Handbook of Mathematical Functions, pp.160-171, 2010.

T. Wang and T. Yi, Uniqueness of positive solutions of the Choquard type equations, Applicable Analysis, vol.27, issue.3, pp.1-9, 2016.
DOI : 10.1007/978-1-4612-4146-1

J. Wei and M. Winter, Strongly interacting bumps for the Schrödinger?Newton equations, J. Math Phys, issue.1, pp.12905-12927, 2009.
DOI : 10.1063/1.3060169

D. Bonheure, D. De-mathématique-di-bari, D. Di-meccanica, . Matematica-e-management, and E. Via, Boulevard du Triomphe, B-1050 Bruxelles, Belgium, and INRIA ? Team MEPHYSTO. E-mail address: denis.bonheure@ulb.ac.be Silvia Cingolani Orabona 4, 70125 Bari, Italy E-mail address: silvia.cingolani@poliba.it Jean Van Schaftingen, 1348.