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Periodic solutions of the Brillouin electron beam focusing equation

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  • Quite unexpectedly with respect to the numerical and analytical results found in literature, we establish a new range for the real parameter $b$ for which the existence of $2\pi-$periodic solutions of the Brillouin focusing beam equation \begin{eqnarray} \ddot{x}+b(1+\cos t)x=\frac{1}{x} \end{eqnarray} is guaranteed. This is possible thanks to suitable nonresonance conditions acting on the rotation number of the solutions in the phase plane.
    Mathematics Subject Classification: Primary: 34B15, 34C25; Secondary: 34B16.


    \begin{equation} \\ \end{equation}
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