Periodic solutions for nonlinear elliptic equations.: Application to charged particle beam focusing systems

被引：0
作者：
Bostan, Mihai [1 ]
Sonnendrucker, Eric [1 ]
机构：
[1] Univ Franche Comte, CNRS, UMR 6623, Lab Math Besancon, F-25030 Besancon, France
来源：
ESAIM-MATHEMATICAL MODELLING AND NUMERICAL ANALYSIS-MODELISATION MATHEMATIQUE ET ANALYSE NUMERIQUE | 2006年 / 40卷 / 06期
关键词：
nonlinear elliptic equations; periodic solutions; existence and uniqueness; electron beam focusing system;
D O I：
10.1051/m2an:2006039
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We study the existence of spatial periodic solutions for nonlinear elliptic equations -Delta u + g( x, u( x)) = 0, x is an element of R-N 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.
引用
收藏
页码：1023 / 1052
页数：30
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