Periodic solutions for nonlinear elliptic equations. Application to charged particle beam focusing systems
Mathématiques de Besançon, UMR CNRS 6623, Université de
Franche-Comté, 16 route de Gray, 25030 Besançon Cedex,
2 IRMA, Université Louis Pasteur, rue René Descartes, 67084 Strasbourg Cedex, France. firstname.lastname@example.org
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.
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