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Periodic solutions for nonlinear elliptic equations.Application to charged particle beam focusing systems
Published online by Cambridge University Press: 15 February 2007
Abstract
We study the existence of spatial periodic solutions for nonlinear elliptic equations $- \Delta u \, + \, g(x,u(x)) = 0, \;x \in {\mathbb R}^N$ 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.
Keywords
- Type
- Research Article
- Information
- ESAIM: Mathematical Modelling and Numerical Analysis , Volume 40 , Issue 6 , November 2006 , pp. 1023 - 1052
- Copyright
- © EDP Sciences, SMAI, 2007