The Choquard equation and related questions. (English) Zbl 0453.47042


47J05 Equations involving nonlinear operators (general)
58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces
35P30 Nonlinear eigenvalue problems and nonlinear spectral theory for PDEs
Full Text: DOI


[1] Ambrosetti, A.; Rabinowitz, P. H., Dual variational methods in critical point theory and applications, J. Funct. Analysis, 14, 349-381 (1973) · Zbl 0273.49063
[2] Aubin, T., Problèmes isopérimétriques et espaces de Sobolev, Comptes Rendus Paris, 280, 279-281 (1975) · Zbl 0295.53024
[3] Berestycki, H.; Lions, P. L., Existence d’ondes solitaires dans des problèmes non linéaires du type Klein-Gordon, Comptes Rendus Paris, 287, 503-506 (1978) · Zbl 0391.35055
[4] Berestycki, H.; Lions, P. P., Existence d’ondes solitaires dans des problèmes non linéaires du type Klein-Gordon: 2 ème partie, Comptes Rendus Paris, 288, 395-398 (1979) · Zbl 0397.35024
[5] Berestycki, H.; Lions, P. L., Existence of a ground state in nonlinear equations of the type Klein-Gordon, (Cottle; Gianessi, Variational Inequalities (1979), J. Wiley: J. Wiley New York), To appear · Zbl 0707.35143
[8] Berger, M. S., On the existence and structure of stationary states for a nonlinear Klein-Gordon equation, J. funct. Analysis, 9, 249-261 (1972) · Zbl 0224.35061
[10] Coffman, C. V., Uniqueness of the ground state for Δu − \(u + u^3 = 0\) and a variational characterization of the other solutions, Archs. ration. Mech. Analysis, 46, 81-95 (1972) · Zbl 0249.35029
[11] Fukuda, I.; Tsutsumi, M., On the Yukawa-coupled Klein-Gordon Schrödinger equations in three space dimensions, Proc. Japan Acad., 51, 402-405 (1975) · Zbl 0313.35065
[12] Fukuda, I.; Tsutsumi, M., On coupled Klein-Gordon Schrödinger equations, J. math. Analysis Applic., 66, 358-378 (1978), ii · Zbl 0396.35082
[13] Krasnoselski, M. A., Topological Methods in the Theory of Nonlinear Integral Equations (1964), Macmillan: Macmillan New York
[14] Lieb, E. H., Existence and uniqueness of the minimizing solution of Choquard’s nonlinear equation, Studies appl. Math., 57, 93-105 (1977) · Zbl 0369.35022
[15] Lieb, E. H.; Simon, B., The Hartree-Fock theory for Coulomb systems, Comm. Math. Phys., 53, 185-194 (1977)
[18] Nehari, Z., On a nonlinear differential equation arising in nuclear physics, Proc. R. Irish Acad., 62, 117-135 (1963) · Zbl 0124.30204
[19] Rabinowitz, P. H., Variational methods for nonlinear eigenvalue problems, (Eigenvalues of Nonlinear Problems (1974), CIME, Edizioni Gremonese: CIME, Edizioni Gremonese Rome) · Zbl 0212.16504
[20] Reeken, M., General theorem on bifurcation and its application to the Hartree equation of the helium atom, J. Math. Phys. vol. 11, 8, 2505-2512 (1970)
[21] Rosen, G., Minimum value for \(c\) in the Sobolev inequality‖\(ϕ\)‖\(_3\) ⩽ \(c\)‖∇\(ϕ\)‖\(_2\), SIAM J. appl. Math., 21, 30-32 (1971) · Zbl 0201.38704
[22] Ryder, G. H., Boundary value problems for a class of nonlinear differenticial equations, Pacif. J. Math., 22, 447-503 (1967) · Zbl 0152.28303
[23] Strauss, W., Existence of solitary waves in higher dimensions, Comm. Math. Phys., 55, 149-162 (1977) · Zbl 0356.35028
[24] Staurt, C. A., Existence theory for the Hartree equation, Archs. ration. Mech. Analysis, 51, 60-69 (1973) · Zbl 0287.34032
[26] Wiegel, F. W., The interacting Bose fluid: path integral representations and renormalization group approach, (Papadopoulos, G. J.; Denease, J. T., Path Integrals (1978), ASI, Plenum Press: ASI, Plenum Press New York) · Zbl 0435.76062
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.