Abstract
An experimental conjecture on the existence of positive periodic solutions for the Brillouin electron beam focusing system x''+a(1+cos 2t)x=frac{1}{x} for ain(0,frac{1}{2}) is proved by applications of the Manasevich-Mawhin theorem.
Highlights
In this paper, we consider the π -periodic boundary value problem for the equation x + a( cos t)x ( . )x where a > is constant.The equations arise in the study of electronics and govern the motion of a magnetically focused axially symmetric electron beam under the influence of a Brillouin flow [ ]
In [ ], Zhang investigated a kind of singular Liénard equation, and by applications of his theory, they extended the existence result of ( . ) to a ∈ (, . )
Authors’ contributions ZBC and SWY worked together in the derivation of the mathematical results
Summary
We consider the π -periodic boundary value problem for the equation x + a( cos t)x ( . )x where a > is constant.The equations arise in the study of electronics and govern the motion of a magnetically focused axially symmetric electron beam under the influence of a Brillouin flow [ ]. Is proved by applications of the Manasevich-Mawhin theorem. Introduction In this paper, we consider the π -periodic boundary value problem for the equation x cos t)x The equations arise in the study of electronics and govern the motion of a magnetically focused axially symmetric electron beam under the influence of a Brillouin flow [ ]. ). Besides, from a mathematical point of view, equation
Sign-in/Register to view highlights & summary Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
