Maslov, V. P. Equations of the self-consistent field. (English) Zbl 0408.45010 J. Sov. Math. 11, 123-195 (1979). Page: −5 −4 −3 −2 −1 ±0 +1 +2 +3 +4 +5 Show Scanned Page Cited in 9 Documents MSC: 45K05 Integro-partial differential equations 35Q99 Partial differential equations of mathematical physics and other areas of application 81Q05 Closed and approximate solutions to the Schrödinger, Dirac, Klein-Gordon and other equations of quantum mechanics 82D10 Statistical mechanics of plasmas 35C05 Solutions to PDEs in closed form 35B45 A priori estimates in context of PDEs 81V70 Many-body theory; quantum Hall effect 45J05 Integro-ordinary differential equations 85A05 Galactic and stellar dynamics Citations:Zbl 0404.45008 × Cite Format Result Cite Review PDF Full Text: DOI References: [1] A. A. Arsen’ev, ”The existence of generalized solutions of the Vlasov equation,” Zh. Vychisl. Mat. Mat. Fiz.,15, 1 (1975). [2] N. Blombergen, Nonlinear Optics, Benjamin, New York (1965). [3] R. Balescu, Statistical Mechanics of Charged Particles, Wiley-Interscience, London-New York (1963). · Zbl 0125.23106 [4] N. N. Bogolyubov, Problems of the Dynamical Theory in Statistical Physics, Moscow-Leningrad (1946). [5] K. P. Gurov, Foundations of Kinetic Theory [in Russian], Nauka, Moscow (1966). [6] Yu. L. Daletskii, ”Continuum integrals related to operator evolution equations,” Usp. Mat. Nauk,17, No. 5, 3–115 (1965). [7] Yu. N. Demkov, Variational Principles in Collision Theory [in Russian], Fizmatgiz, Moscow (1958). · Zbl 0111.42806 [8] Yu. L. Klimantovich, Kinetic Theory of a Nonideal Gas and Nonideal Plasma [in Russian], Nauka, Moscow (1975). [9] V. P. Maslov, Complex Markov Chains and the Continuum Integral of Feynman for Nonlinear Equations [in Russian], Nauka, Moscow (1976). [10] V. P. Maslov, Operator Methods [in Russian], Nauka, Moscow (1973). [11] A. M. Chebotarev, ”The representation of the solution of an equation of Hartree type in the form of a T-mapping,” Dokl. Akad. Nauk SSSR,222, No. 5, 1037–1040 (1975). [12] A. A. Sokolov, Yu. M. Loskutov, and I. M. Ternov, Quantum Mechanics [in Russian], Uchpedgiz, Moscow (1962). [13] R. Feynman and A. Hibbs, Quantum Mechanics and Path Integrals, McGraw-Hill, New York (1965). · Zbl 0176.54902 [14] V. A. Fok, Works on Quantum Field Theory, 4th Ed., Leningrad (1957). [15] E. S. Fradkin, ”The method of Green functions in quantum field theory and statistics,” Tr. Fiz. Inst. Akad. Nauk,29, 1–130 (1965). [16] E. Hille and R. Phillips, Functional Analysis and Semigroups, Amer. Math. Soc., Providence (1957). · Zbl 0078.10004 [17] S. A. Achmanov, R. V. Hochlov, and A. P. Suchorukov, ”Self-Defocusing and self-modulation in nonlinear media,” Laserhandbuch, Vol. 2, North-Holland (1972), pp. 5–108. [18] T. Kato, ”Quasilinear equations of evolution with applications to partial differential equations,” Lect. Notes Math.,448, 25–70 (1975). · doi:10.1007/BFb0067080 [19] E. Nelson, ”Feynman integrals and the Schrödinger equation,” J. Math. Phys.,5, No. 3, 332–343 (1964). · Zbl 0133.22905 · doi:10.1063/1.1704124 [20] H. F. Trotter, ”On the product of semigroups of operators,” Proc. Am. Math. Soc.,10, No. 4, 545–551 (1959). · Zbl 0099.10401 · doi:10.1090/S0002-9939-1959-0108732-6 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.