Solitary waves for Maxwell-Schrödinger equations

Electronic Journal of Differential Equations

Volumn 2004, Issue , 2004, Pages 1-15

  Coclite, Giuseppe Maria ^a   Georgiev, Vladimir ^b  

^a CMA   (Norway)

^b UNIVERSITY OF PISA   (Italy)

Author keywords

Maxwell Schr dinger system; Solitary type solutions; Variational problems

Indexed keywords

EID: 4644344610     PISSN: 10726691     EISSN: None     Source Type: Journal    
DOI: None     Document Type: Article

References (25)

1. Agemi R., Kubota K., Takamura H.: On certain integral equations related to nonlinear wave equations. Hokkaido Math. J., 241-276 (1994).
2. Agmon S. Lower bounds for solutions of Schrödinger equations, J. Anal. Math. 1-25 (1970).
3. Ambrosetti A., Rabinowitz P. H.: Dual variational methods in critical point theory and applications, J. Funct. Analysis, 14, 349-381 (1973).
4. Avron J., Herbsit I., Simon B.: Schrödinger operators with magnetic fields I. General interaction Duke Math. J. 45, 847-883 (1978).
5. Avron J., Herbsit I., Simon B.: Schrödinger operators with magnetic fields I. Atoms in homogeneous magnetic fields Comm. Math. Phys. 79, 529-572 (1981).
6. Benci V., Fortunato D.: An eigenvalue problem for the Schrödinger Maxwell equations Topological Methods in Nonlinear Analysis 11 , 283-293 (1998).
7. Benci V., Fortunato D.: Solitary waves of the nonlinear Klein-Gordon equation coupled with the Maxwell equations, Rev. Math. Phys. 4, 409-420 (2002).
8. Beresticki H., Lions P. L.: Nonlinear scalar field equations. I Existence of a ground state Arch. Rational Mech. Anal. 82, 313-346 (1983).
9. Born M., Atomic Physics, (Blackie and Son Limited, London - Glasgow, 1969).
10. Coclite G. M.: A multiplicity result for the nonlinear Schrödinger - Maxwell equations Communications on Applied Analysis 7 vol. 2-3, 417-423 (2003).
11. Coclite G. M.: A multiplicity result for the Schrödinger - Maxwell equations, Annales Polonici Mathematici 79 vol. 1, 21-30 (2002).
12. Coclite G. M.: Metodi Variazionali Applicati allo Studio delle Equazioni di Schrödinger-Maxwell, graduate thesis, University of Bari (1999).
13. Combes J. M., Schrader R. , Seiler R.: Classical bounds and limits for energy distributions of Hamiltonian operators in electromagnetic fields, Ann. Phys. 111 1-18 (1978).
14. Esteban M. J., Georgiev V., Sere E.: Stationary solutions of the Maxwell-Dirac and the Klein-Gordon-Dirac equations, Calc. Var. 4 265-281 (1996).
15. Hardy G., Litllewood G., Polya G. , Inequalities, (Cambridge University Press, 1948).
16. Komech A., Mauser N., Lectures on Classical Fields and Quantum Mechanics. Part I (Wien 2002-2003).
17. Lieb E. The Stability of Matter: From Atoms to Stars (Springer, 1997).
18. Lions P. L.: Solutions of Hartree-Fock Equations for Coulomb Systems, Commun. Math. Phys. 109, 33 - 97 (1987).
19. Palais R. S.: The principle of symmetric criticality, Commun. Math. Phys. 69, 19-30 (1979).
20. Rabinowitz P. H.: Variational methods for nonlinear eigenvalue problems, Proc. CIME (1974), 139-195.
21. Reed M., Simon B.: Methods of Modern Mathematical Physics, vol. II, Fourier Analysis and Self Adjointness, Academic Press, New York, San Francisco, London, 1975.
22. Sokolov A. A., Ternov I. M., Zukowski V. Ch., Quantum mechanics (Nauka, 1979).
23. Strauss W. A.: Existence of solitary waves in higher dimensions, Commun. Math. Phys. 55, 149-162 (1977).
24. Triebel H.: Interpolation Theory, Function Spaces, Differential Operators, (North Holland Co., Amsterdam, 1978).
25. Willem M.: Minimax Theorems, (Birkhuser, Boston, 1996).