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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.

MSC:
34C25 Periodic solutions to ordinary differential equations
34C60 Qualitative investigation and simulation of ordinary differential equation models
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References:
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