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 2π-periodic solutions of the Brillouin focusing beam equation ẍ + b(1 + cos t)x =1/x is guaranteed. This is possible thanks to suitable nonresonance conditions acting on the rotation number of the solutions in the phase plane.
Garrione, M., Zamora, M. (2014). Periodic solutions of the Brillouin electron beam focusing equation. COMMUNICATIONS ON PURE AND APPLIED ANALYSIS, 13(2), 961-975 [10.3934/cpaa.2014.13.961].
Periodic solutions of the Brillouin electron beam focusing equation
GARRIONE, MAURIZIO
;
2014
Abstract
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 2π-periodic solutions of the Brillouin focusing beam equation ẍ + b(1 + cos t)x =1/x is guaranteed. This is possible thanks to suitable nonresonance conditions acting on the rotation number of the solutions in the phase plane.
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