A. Azzollini, P. d’Avenia and A. Pomponio, On the Schrödinger–Maxwell equations under the effect of a general nonlinear term, Ann. Inst. H. Poincaré Anal. Non Linéaire 27 (2010), 779–791.

V. Benci and D. Fortunato, Solitary waves of the nonlinear Klein–Gordon equation coupled with the Maxwell equations, Rev. Math. Phys. 14 (2002), 409–420.

H. Berestycki and P.-L. Lions, Nonlinear scalar field equations I. Existence of a ground state, Arch. Rational Mech. Anal. 82 (1983), 313–345.

H. Brézis and E. Lieb, A relation between pointwise convergence of functions and convergence of functionals, Proc. Amer. Math. Soc. 88 (1983), 486–490.

P. Choquard, J. Stubbe and M. Vuffray, Stationary solutions of the Schrödinger–Newton model-an ODE approach, Differential Integral Equations 21 (2008), 665–679.

T. D’Aprile and D. Mugnai, Non-existence results for the coupled Klein–Gordon–Maxwell equations, Adv. Nonlinear Stud. 4 (2004), 307–322.

L. Jeanjean, On the existence of bounded Palais–Smale sequences and application to a Landesman–Lazer-type problem set on RN , Proc. Roy. Soc. Edinburgh Sect. A 129 (1999), 787–809.

L. Jeanjean and K. Tanaka, A remark on least energy solutions in RN , Proc. Amer. Math. Soc. 131 (2003), 2399–2408.

C. Keller, Large-time asymptotic behavior of solutions of nonlinear wave equations perturbed from a stationary ground state, Comm. Partial Differential Equations 8 (1983), 1073–1099.

E. H. Lieb, Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation, Studies in Appl. Math. 57 (1976/77), 93–105.

E.H. Lieb and M. Loss, Analysis, second edition, Graduate Studies in Mathematics, vol. 14, American Mathematical Society, Providence, RI, 2001.

P.-L. Lions, The Choquard equation and related questions, Nonlinear Anal. 4 (1980), 1063–1072.

P.-L. Lions, The concentration-compactness principle in the calculus of variations. The locally compact case II, Ann. Inst. H. Poincaré Anal. Non Linéaire 1 (1984), 223–283.

G.P. Menzala, On regular solutions of a nonlinear equation of Choquard’s type, Proc. Roy. Soc. Edinburgh Sect. A 86 (1980), 291–301.

I.M. Moroz, R. Penrose and P. Tod, Spherically-symmetric solutions of the Schrödinger–Newton equations, Topology of the Universe Conference (Cleveland, OH, 1997), Classical Quantum Gravity 15 (1998), 2733–2742.

V. Moroz and J. Van Schaftingen, Groundstates of nonlinear Choquard equations: existence, qualitative properties and decay asymptotics, J. Funct. Anal. 265 (2013), 153–184.

V. Moroz and J. Van Schaftingen, Existence of groundstates for a class of nonlinear Choquard equations, Trans. Amer. Math. Soc. 367 (2015), 6557–6579.

V. Moroz and J. Van Schaftingen, A guide to the Choquard equation, J. Fixed Point Theory Appl. 19 (2017), 773–813.

S. Pekar, Untersuchung über die Elektronentheorie der Kristalle, Akademie Verlag, Berlin, 1954.

D. Qin, V.D. Rădulescu and X. Tang, Ground states and geometrically distinct solutions for periodic Choquard–Pekar equations, J. Differential Equations 275 (2021), 652–683.

D. Ruiz, The Schrödinger–Poisson equation under the effect of a nonlinear local term, J. Funct. Anal. 237 (2006), 655–674.

J. Shatah, Unstable ground state of nonlinear Klein–Gordon equations, Trans. Amer. Math. Soc. 290 (1985), 701–710.

M. Struwe, Variational Methods. Applications to Nonlinear Partial Differential Equations and Hamiltonian systems, fourth edition, Springer–Verlag, Berlin, 2008.

P. Tod and I.M. Moroz, An analytical approach to the Schrödinger–Newton equations, Nonlinearity 12 (1999), 201–216.

Z.-Q. Wang and J. Xia, Saddle solutions for the Choquard equation II, Nonlinear Anal. 201 (2020), 112053, 25 pp.

M. Willem, Minimax Theorems. Progress in Nonlinear Differential Equations and their Applications, vol. 24, Birkhäuser Boston, Inc., Boston, MA, 1996.

L. Zhao and F. Zhao, On the existence of solutions for the Schrödinger–Poisson equations, J. Math. Anal. Appl. 346 (2008), 155–169.