| Issue |
ESAIM: M2AN
Volume 40, Number 6, November-December 2006
|
|
|---|---|---|
| Page(s) | 1023 - 1052 | |
| DOI | https://doi.org/10.1051/m2an:2006039 | |
| Published online | 15 February 2007 | |
Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems
1
Laboratoire de
Mathématiques de Besançon, UMR CNRS 6623, Université de
Franche-Comté, 16 route de Gray, 25030 Besançon Cedex,
France. mbostan@math.univ-fcomte.fr
2
IRMA, Université Louis Pasteur, rue
René Descartes, 67084 Strasbourg Cedex, France.
sonnen@math.u-strasbg.fr
Received:
10
April
2006
We study the existence of spatial periodic solutions for nonlinear
elliptic equations 
where g is a continuous function, nondecreasing w.r.t. u. We
give necessary and sufficient conditions for the existence of
periodic solutions. Some cases with nonincreasing functions g
are investigated as well. As an application we analyze the
mathematical model of electron beam focusing system and we prove
the existence of positive periodic solutions for the envelope
equation. We present also numerical simulations.
Mathematics Subject Classification: 35A05 / 35B35
Key words: Nonlinear elliptic equations / periodic solutions / existence and uniqueness / electron beam focusing system.
© EDP Sciences, SMAI, 2007
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