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Existence of positive periodic solution for the electron beam focusing system. (English) Zbl 1069.34065
Summary: We study the mathematical model of electron beam focusing system \[ y''+ a(1+ \cos 2x)y= {1\over y}+{b\over y^3}, \] where \(a> 0\), \(b\geq 0\) are constants, and find conditions for the existence of positive \(\pi\)-periodic solution of the above equation by using analytical method and comparison theory, and prove the existence of a positive \(\pi\)-periodic solution by the continuously dependent theory of an initial value problem.

34C25 Periodic solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
Full Text: DOI
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