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.
Articolo in rivista - Articolo scientifico
Brillouin focusing system; Periodic solutions; Poincaré-Bohl theorem; Singular nonlinearities; Analysis; Applied Mathematics
English
2014
13
2
961
975
none
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].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10281/62290
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