# American Institute of Mathematical Sciences

September  2013, 18(7): 1995-1997. doi: 10.3934/dcdsb.2013.18.1995

## An erratum note on the paper: Positive periodic solution for Brillouin electron beam focusing system

 1 School of Mathematical Sciences, Capital Normal University, Beijing 100048 2 School of Mathematical Sciences, Capital Normal University, Beijing, 100048, China 3 School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China

Received  September 2012 Revised  April 2013 Published  May 2013

In this paper, we point out an error in the paper: Positive periodic solution for Brillouin electron beam focusing system, Discrete Contin. Dyn. Syst. Ser. B, 16(2011), 385-392. Meanwhile, it is pointed out that, for $0 < a < 1$, the conjecture that the Brillouin electron beam focusing system $x''+a(1+\cos 2t)x=1/x$ admits positive periodic solutions is still an open problem.
Citation: Zaihong Wang, Jin Li, Tiantian Ma. An erratum note on the paper: Positive periodic solution for Brillouin electron beam focusing system. Discrete & Continuous Dynamical Systems - B, 2013, 18 (7) : 1995-1997. doi: 10.3934/dcdsb.2013.18.1995
##### References:
 [1] J. Ren, Z. Cheng and S. Siegmund, Positive periodic solution for Brillouin electron beam focusing system,, Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 385. doi: 10.3934/dcdsb.2011.16.385. Google Scholar [2] V. Bevc, J. L. Palmer and C. Süsskind, On the design of the transition region of axisymmetric magnetically focused beam values,, J. British Inst. Radio Engineers, 18 (1958), 696. Google Scholar [3] R. Ortega, Periodic perturbations of an isochronous center,, Qual. Theory Dyn. Syst., 3 (2002), 83. doi: 10.1007/BF02969334. Google Scholar [4] D. Bonheure, C. Fabry and D. Smets, Periodic solutions of forced isochronous oscillators at resonance,, Discrete Contin. Dyn. Syst., 8 (2002), 907. doi: 10.3934/dcds.2002.8.907. Google Scholar [5] T. Ding, A boundary value problem for the periodic Brillouin focusing system,, Acta Sci. Natur. Univ. Pekinensis, 11 (1965), 31. Google Scholar [6] Y. Ye and X. Wang, Nonlinear differential equations in electron beam focusing theory,, Acta Math. Appl. Sinica, 1 (1978), 13. Google Scholar [7] M. R. Zhang, A relationship between the periodic and the Dirichlet BVPs of singular differential equation,, Proc. Roy. Soc. Edinburgh, 128 (1998), 1099. doi: 10.1017/S0308210500030080. Google Scholar

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##### References:
 [1] J. Ren, Z. Cheng and S. Siegmund, Positive periodic solution for Brillouin electron beam focusing system,, Discrete Contin. Dyn. Syst. Ser. B, 16 (2011), 385. doi: 10.3934/dcdsb.2011.16.385. Google Scholar [2] V. Bevc, J. L. Palmer and C. Süsskind, On the design of the transition region of axisymmetric magnetically focused beam values,, J. British Inst. Radio Engineers, 18 (1958), 696. Google Scholar [3] R. Ortega, Periodic perturbations of an isochronous center,, Qual. Theory Dyn. Syst., 3 (2002), 83. doi: 10.1007/BF02969334. Google Scholar [4] D. Bonheure, C. Fabry and D. Smets, Periodic solutions of forced isochronous oscillators at resonance,, Discrete Contin. Dyn. Syst., 8 (2002), 907. doi: 10.3934/dcds.2002.8.907. Google Scholar [5] T. Ding, A boundary value problem for the periodic Brillouin focusing system,, Acta Sci. Natur. Univ. Pekinensis, 11 (1965), 31. Google Scholar [6] Y. Ye and X. Wang, Nonlinear differential equations in electron beam focusing theory,, Acta Math. Appl. Sinica, 1 (1978), 13. Google Scholar [7] M. R. Zhang, A relationship between the periodic and the Dirichlet BVPs of singular differential equation,, Proc. Roy. Soc. Edinburgh, 128 (1998), 1099. doi: 10.1017/S0308210500030080. Google Scholar
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