We study the existence of spatial periodic solutions for nonlinear elliptic equations where is a continuous function, nondecreasing w.r.t. . We give necessary and sufficient conditions for the existence of periodic solutions. Some cases with nonincreasing functions 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.
Mots-clés : nonlinear elliptic equations, periodic solutions, existence and uniqueness, electron beam focusing system
@article{M2AN_2006__40_6_1023_0,
author = {Bostan, Mihai and Sonnendr\"ucker, Eric},
title = {Periodic solutions for nonlinear elliptic equations. {Application} to charged particle beam focusing systems},
journal = {ESAIM: Mod\'elisation math\'ematique et analyse num\'erique},
pages = {1023--1052},
publisher = {EDP-Sciences},
volume = {40},
number = {6},
year = {2006},
doi = {10.1051/m2an:2006039},
mrnumber = {2297103},
zbl = {1133.78307},
language = {en},
url = {http://www.numdam.org/articles/10.1051/m2an:2006039/}
}
TY - JOUR AU - Bostan, Mihai AU - Sonnendrücker, Eric TI - Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems JO - ESAIM: Modélisation mathématique et analyse numérique PY - 2006 SP - 1023 EP - 1052 VL - 40 IS - 6 PB - EDP-Sciences UR - http://www.numdam.org/articles/10.1051/m2an:2006039/ DO - 10.1051/m2an:2006039 LA - en ID - M2AN_2006__40_6_1023_0 ER -
%0 Journal Article %A Bostan, Mihai %A Sonnendrücker, Eric %T Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems %J ESAIM: Modélisation mathématique et analyse numérique %D 2006 %P 1023-1052 %V 40 %N 6 %I EDP-Sciences %U http://www.numdam.org/articles/10.1051/m2an:2006039/ %R 10.1051/m2an:2006039 %G en %F M2AN_2006__40_6_1023_0
Bostan, Mihai; Sonnendrücker, Eric. Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems. ESAIM: Modélisation mathématique et analyse numérique, Tome 40 (2006) no. 6, pp. 1023-1052. doi : 10.1051/m2an:2006039. http://www.numdam.org/articles/10.1051/m2an:2006039/
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