Positive periodic solution for Brillouin electron beam focusing system

Jingli Ren; Zhibo Cheng; Stefan Siegmund

doi:10.3934/dcdsb.2011.16.385

Article Contents

2011, Volume 16, Issue 1: 385-392. Doi: 10.3934/dcdsb.2011.16.385

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Positive periodic solution for Brillouin electron beam focusing system

1.
Dept. of Math., Zhengzhou University, Zhengzhou 450001
2.
Dept. of Math., Dresden University of Technology, Dresden 01062

Received: February 28, 2010

Revised: June 30, 2010

Published: June 2011

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Abstract

An experimental conjecture on the existence of positive periodic solutions for the Brillouin electron beam focusing system $x''+a(1+\cos2t)x=\frac{1}{x}$ for $0 < a < 1$ is proved, using a topological degree theorem by Mawhin.

Keywords:

Brillouin electron beam focusing system,
Liénard equation,
singularity.

Mathematics Subject Classification: Primary: 34B27; Secondary: 37C55.

Citation:

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References

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