Lions, Pierre-Louis Some remarks on Hartree equation. (English) Zbl 0472.35074 Nonlinear Anal., Theory Methods Appl. 5, 1245-1256 (1981). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 1 ReviewCited in 44 Documents MSC: 35Q99 Partial differential equations of mathematical physics and other areas of application 47J10 Nonlinear spectral theory, nonlinear eigenvalue problems 58E05 Abstract critical point theory (Morse theory, Lyusternik-Shnirel’man theory, etc.) in infinite-dimensional spaces Keywords:nonlocal semilinear problems; nonlinear eigenvalue problems; Hartree equation; critical point theory × Cite Format Result Cite Review PDF Full Text: DOI References: [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] Bader, P., Variational method for the Hartree equation of the helium atom, Proc. R. Phys. Soc. Edinb., 82A, 27-39 (1978) · Zbl 0403.45021 [3] Bazley, N.; Seydel, R., Existence and bounds for critical energies of the Hartree equation, Chem. Phys. Lett., 24, 1, 128-132 (1974) [4] Bazley, N.; Zwahlen, B., A branch of positive solutions of non-linear eigenvalue problems, Manuscripta Math., 2, 365-374 (1970) · Zbl 0192.49501 [5] Berestycki H., Le nombre de solutions de certains problèmes elliptiques semilinéaires. To appear in J. funct. Analysis.; Berestycki H., Le nombre de solutions de certains problèmes elliptiques semilinéaires. To appear in J. funct. Analysis. [6] Berestycki, H.; Lions, P. L., Existence d’ondes solitaires dans des problèmes non linéaires du type Klein-Gordon. II., Compte-Rendus Paris, 396-398 (1979) · Zbl 0397.35024 [7] Berestycki, H.; Lions, P. L., Nonlinear scalar fields equations, II, Archs ration. Mech. Analysis (1981), To appear in [8] Gustafson, K.; Sather, D., Branching analysis of the Hartree equations, Rend. di Mat., 4, 723-734 (1971) [9] Hartree, D., The wave mechanics of an atom with a non-Coulomb central field. Part I. Theory and methods, Proc. Camb. phil. Soc., 24, 89-132 (1928) · JFM 54.0966.05 [10] Helling, G., Differential Operators of Mathematical Physics (1967), Addison-Wesley: Addison-Wesley Reading · Zbl 0163.11801 [11] Kato, T., Perturbation Theory for Linear Operators (1966), Springer: Springer Berlin-Heidelberg, New York · Zbl 0148.12601 [12] Lieb, E. H., Existence and uniqueness of minimizing solutions of Choquard’s non-linear equation, Studies appl. Math., 57, 93-105 (1977) · Zbl 0369.35022 [13] Lieb, E. H.; Simon, B., The Hartree-Fock theory for Coulomb systems, Commun. math. Phys., 53, 185-194 (1974) [14] Lions, P. L., The Choquard equation and related questions, J. Nonlinear Analysis, 1063-1072 (1980) · Zbl 0453.47042 [15] Rabinowitz, P. H., Some global results for nonlinear eigenvalue problems, J. funct. analaysis, 7, 487-513 (1971) · Zbl 0212.16504 [16] Rabinowitz, P. H., Variational methods for nonlinear eigenvalue problems, (Eigenvalues of Nonlinear Problems (1974), CIME-Cremonese: CIME-Cremonese Rome) · Zbl 0212.16504 [17] Reeken, M., Global theorem on bifurcation and its application to the Hartree equation of the helium atom, J. Math. Phys., 11, 2505-2512 (1970) [18] Slater, J. C., A note on Hartree’s method, Phys. Rev., 35, 210-211 (1930) [19] Stuart, C. A., Existence theory for the Hartree equation, Archs. ration. Mech. Analysis, 51, 60-69 (1973) · Zbl 0287.34032 [20] Stuart, C. A., An example in nonlinear functional analysis: the Hartree equation, J. math. Analysis Applic., 49, 3, 725-733 (1975) · Zbl 0311.47032 [21] Titchmarsh, E. C., Eigenfunction Expansions (1962), Oxford Univ. Press: Oxford Univ. Press London, Part II · Zbl 0099.05201 [22] Wolkowisky, J., Existence of solutions of the Hartree equations for \(N\) electrons. An aoplication of the Schauder-Tychonoff theorem, Indiana Univ. Math. J., 22, 551-558 (1972) · Zbl 0237.34006 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.