@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}, pages = {229--244}, publisher = {Gauthier-Villars}, volume = {68}, number = {2}, year = {1998}, mrnumber = {1618672}, zbl = {0907.35104}, language = {en}, url = {http://www.numdam.org/item/AIHPA_1998__68_2_229_0/} }
TY - JOUR AU - Abenda, Simonetta TI - Solitary waves for Maxwell-Dirac and Coulomb-Dirac models JO - Annales de l'I.H.P. Physique théorique PY - 1998 SP - 229 EP - 244 VL - 68 IS - 2 PB - Gauthier-Villars UR - http://www.numdam.org/item/AIHPA_1998__68_2_229_0/ LA - en ID - AIHPA_1998__68_2_229_0 ER -
Abenda, Simonetta. Solitary waves for Maxwell-Dirac and Coulomb-Dirac models. Annales de l'I.H.P. Physique théorique, Tome 68 (1998) no. 2, pp. 229-244. http://www.numdam.org/item/AIHPA_1998__68_2_229_0/
[1] Dual Variational methods in critical points theory and applications in J. Funct. Anal., Vol. 14, 1973, pp. 349-381. | MR | Zbl
and ,[2] Existence of standing waves for Dirac fields with singular nonlinearities. Comm. Math. Phys., Vol. 133, 1990, pp. 53-74. | MR | Zbl
, and ,[3] Existence of excited states for a nonlinear Dirac field., Comm. Math. Phys., 119, 1988, pp. 153-176. | MR | Zbl
, , and ,[4] Solutions faibles sous des conditions d'énergie pour des équations de champ.
and ,[5] Critical point theorems for indefinite functionals. Inv. Math., Vol. 52, 1979, pp. 336-352. | MR | Zbl
and ,[6] Relativistic quantum fields. McGraw-Hill, 1965. | MR | Zbl
and ,[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] Existence of localized solutions for a classical nonlinear Dirac field. Comm. Math. Phys., Vol. 105, 1986, pp. 35-47. | MR | Zbl
and ,[9] Un criterio di esistenza per i punti critici su varietá illimitate Ist. Lomb. (Rend. Sc.), Vol. A 112, 1978, pp. 332-336. | Zbl
,[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 | Zbl
,[11] 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 | Zbl
and ,[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 | Zbl
,[13] Stationary solutions of the Maxwell-Dirac and Klein-Gordon-Dirac equations. To appear, 1995. | MR
, and ,[14] 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 | Zbl
and ,[ 15] Stationary states of the nonlinear Dirac equation : a variational approach. Comm. Math. Phys., Vol. 171, 1995, pp. 323-348. | MR | Zbl
and ,[16] On the global solutions of the Maxwell-Dirac equations. Comm. Math. Physics, Vol. 113, 1987, pp. 21-49. | MR | Zbl
, and ,[17] A solitary wave solution of the Maxwell-Dirac equations , University of California at San Diego, preprint 1995. | MR
,[18] Small amplitude solutions of the Maxwell-Dirac equations. Indiana Univ. Math. J., Vol. 40(3), 1991, pp. 845-883. | MR | Zbl
,[ 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 | Zbl
,[21 ] First order elliptic systems and the existence of homoclinic orbits in Hamiltonian systems. Math. Ann., Vol. 288 (1990, pp. 483-503. | MR | Zbl
and ,[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
,[23] Existence of stationary states for nonlinear Dirac equations. J. Diff. Eq., Vol. 74(1), 1988, pp. 50-68. | MR | Zbl
,[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 | Zbl
,[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 | Zbl
,[28] Nontrivial solution of a semilinear Schrödinger equation, 1994 to appear. | MR | Zbl
and ,[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
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