@article{AIHPA_1998__68_2_229_0,
author = {Abenda, Simonetta},
title = {Solitary waves for Maxwell-Dirac and Coulomb-Dirac models},
journal = {Annales de l'I.H.P. Physique th\'eorique},
volume = {69},
year = {1998},
pages = {229-244},
mrnumber = {1618672},
zbl = {0907.35104},
language = {en},
url = {http://dml.mathdoc.fr/item/AIHPA_1998__68_2_229_0}
}
Abenda, Simonetta. Solitary waves for Maxwell-Dirac and Coulomb-Dirac models. Annales de l'I.H.P. Physique théorique, Tome 69 (1998) pp. 229-244. http://gdmltest.u-ga.fr/item/AIHPA_1998__68_2_229_0/
[1] and , Dual Variational methods in critical points theory and applications in J. Funct. Anal., Vol. 14, 1973, pp. 349-381. | MR 370183 | Zbl 0273.49063
[2] , and , Existence of standing waves for Dirac fields with singular nonlinearities. Comm. Math. Phys., Vol. 133, 1990, pp. 53-74. | MR 1071235 | Zbl 0721.35065
[3] , , and , Existence of excited states for a nonlinear Dirac field., Comm. Math. Phys., 119, 1988, pp. 153-176. | MR 968485 | Zbl 0696.35158
[4] and , Solutions faibles sous des conditions d'énergie pour des équations de champ.
[5] and , Critical point theorems for indefinite functionals. Inv. Math., Vol. 52, 1979, pp. 336-352. | MR 537061 | Zbl 0465.49006
[6] and , Relativistic quantum fields. McGraw-Hill, 1965. | MR 187642 | Zbl 0184.54201
[7] , On the existence of stationary states for classical nonlinear Dirac fields. In Hyperbolic systems and Mathematical Physics. Textos e Notas, Vol. 4, CMAF, Lisbonne, 1989.
[8] and , Existence of localized solutions for a classical nonlinear Dirac field. Comm. Math. Phys., Vol. 105, 1986, pp. 35-47. | MR 847126 | Zbl 0596.35117
[9] , Un criterio di esistenza per i punti critici su varietá illimitate Ist. Lomb. (Rend. Sc.), Vol. A 112, 1978, pp. 332-336. | Zbl 0436.58006
[10] , Global solutions of the Cauchy problem for the (classical) coupled Maxwell-Dirac system in one space dimension. J. Funct. Anal., Vol. 13, 1973, pp. 173-184. | MR 368640 | Zbl 0264.35058
[11] and , On the Maxwell-Dirac equations with zero magnetic field and their solutions in two space dimension. J. Math. Anal. Appl., Vol. 53, 1976, pp. 495-507. | MR 413833 | Zbl 0324.35076
[12] , Solutions globales des équations de Maxwell-Dirac-Klein-Gordon (masses nulles). C.R. Acad. Sci. Paris, Série I, Vol. 292, 1981, pp. 153-158. | MR 610307 | Zbl 0498.35053
[13] , and , Stationary solutions of the Maxwell-Dirac and Klein-Gordon-Dirac equations. To appear, 1995. | MR 1344729
[14] and , Existence de solutions stationnaires pour l'équation de Dirac non-linéaire et le système de Dirac-Poisson. To appear in C. R. Acad. Sci., Série I, 1994. | MR 1309103 | Zbl 0815.35103
[ 15] and , Stationary states of the nonlinear Dirac equation : a variational approach. Comm. Math. Phys., Vol. 171, 1995, pp. 323-348. | MR 1344729 | Zbl 0843.35114
[16] , and , On the global solutions of the Maxwell-Dirac equations. Comm. Math. Physics, Vol. 113, 1987, pp. 21-49. | MR 904136 | Zbl 0641.35064
[17] , A solitary wave solution of the Maxwell-Dirac equations , University of California at San Diego, preprint 1995. | MR 1364144
[18] , Small amplitude solutions of the Maxwell-Dirac equations. Indiana Univ. Math. J., Vol. 40(3), 1991, pp. 845-883. | MR 1129332 | Zbl 0754.35171
[ 19] , Relativistic Quantum Mechanics of Leptons and Fields. Kluwer Acad. Publisher, Fund. Theories of Physics, Vol. 41.
[20] , The Cauchy problem for the coupled Maxwell and Dirac equations. Comm. Pure Appl. Math., Vol. 19, 1966, pp. 1-5. | MR 190520 | Zbl 0137.32401
[21 ] and , First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems. Math. Ann., Vol. 288 (1990, pp. 483-503. | MR 1079873 | Zbl 0702.34039
[22] , The concentration-compactness method in the Calculus of Variations. The locally compact case. Part. I: Anal. non-linéaire, Ann. IHP, Vol. 1, 1984, pp. 109-145. Part. II: Anal. non-linéaire, Ann. IHP, Vol. 1, 1984, pp. 223-283. | Numdam | Zbl 0541.49009
[23] , Existence of stationary states for nonlinear Dirac equations. J. Diff. Eq., Vol. 74(1), 1988, pp. 50-68. | MR 949625 | Zbl 0696.35154
[24] , Classical nonlinear Dirac field models of extended particles. In Quantum theory, groups, fields and particles (editor A.O. Barut). Reidel, Amsterdam, 1982.
[25] , Homoclinic orbits on compact hypersurfaces in R2N, of restricted contact type. Comm. Math. Phys., Vol. 172, 1995, pp. 293-313. | MR 1350410 | Zbl 0840.34046
[26] , Phys. Rev. D1, 1970, pp. 2766-2769.
[27] , Homoclinic orbits in a first order superquadratic Hamiltonian system : convergence of subharmonics. Journ. Diff. Eq., Vol. 94, 1991, pp. 315-339. | MR 1137618 | Zbl 0787.34041
[28] and , Nontrivial solution of a semilinear Schrödinger equation, 1994 to appear. | MR 1410836 | Zbl 0864.35036
[29] , Intensely localized solutions of the classical Dirac-Maxwell field equations. Progr. Theor. Phys., Vol. 35(6), 1966, pp. 1117-1141.
[30] , Minimax theorems, to appear. | MR 1400007