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Positive periodic solution for Brillouin electron beam focusing system

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  • An experimental conjecture on the existence of positive periodic solutions for the Brillouin electron beam focusing system $x''+a(1+\cos2t)x=\frac{1}{x}$ for $0 < a < 1$ is proved, using a topological degree theorem by Mawhin.
    Mathematics Subject Classification: Primary: 34B27; Secondary: 37C55.


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  • [1]

    V. Bevc, J. L. Palmer and C. Süsskind, On the design of the transition region of axisymmetric, magnetically focused beam valves, J. British Inst. Radio Engineer, 18 (1958), 696-708.


    T. R. Ding, "Applications of Qualitative Methods of Ordinary Differential Equations," Higher Education Press, BeiJing, 2004.


    T. R. Ding, A boundary value problem for the periodic Brillouin focusing system, Acta Sci. Natru. Univ. Pekinensis, 11 (1965), 31-38.


    Weigao Ge, "Boundary Value Problems for Nonlinear Ordinary Differential Equations," Science Press, 2007.


    J. Mawhin, Topological degree and boundary value problems for nonlinear differental equations, Topological Methods for Ordinary Differential Equations, 1537 (1993), 74-142.doi: 10.1007/BFb0085076.


    P. J. Torres, Existence and uniquenness of elliptic periodic solutions of the Brillouin electron beam focusing system, Math. Meth. Appl. Sci., 23 (2000), 1139-1143.doi: 10.1002/1099-1476(20000910)23:13<1139::AID-MMA155>3.0.CO;2-J.


    Y. Ye and X. Wang, Nonlinear differential equations in electron beam focusing theory, Acta Math. Appl. Sinica, 1 (1978), 13-41.


    M. R. Zhang, Periodic solutions of Liénard equations with singular forces of repulsive type, J. Math. Anal. Appl., 203 (1996), 254-269.doi: 10.1006/jmaa.1996.0378.


    M. R. Zhang, Nonuniform nonresonance at the first eigenvalue of the $p$-Laplacian, Nonlinear Analysis TMA, 29 (1997), 41-51.doi: 10.1016/S0362-546X(96)00037-5.

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