Electron. J. Diff. Eqns., Vol. 2004(2004), No. 94, pp. 1-31.

Solitary waves for Maxwell-Schrodinger equations

Giuseppe Maria Coclite, Vladimir Georgiev

In this paper we study solitary waves for the coupled system of Schrodinger-Maxwell equations in the three-dimensional space. We prove the existence of a sequence of radial solitary waves for these equations with a fixed L^2 norm. We study the asymptotic behavior and the smoothness of these solutions. We show also that the eigenvalues are negative and the first one is isolated.

Submitted May 21, 2004. Published July 30, 2004.
Math Subject Classifications: 35Q55, 35Q60, 35Q40.
Key Words: Maxwell-Schrodinger system; solitary type solutions; variational problems.

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Giuseppe Maria Coclite
C.M.A. (Centre of Mathematics for Applications)
P.O. Box 1053 Blindern, 0316 Oslo, Norway
email: giusepc@math.uio.no
Vladimir Georgiev
Dipartimento di Matematica
Universita degli Studi di Pisa
Via F. Buonarroti 2, 56100 Pisa, Italy
email: georgiev@dm.unipi.it

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