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Positive periodic solution for Brillouin electron beam focusing system
| 1. | Dept. of Math., Zhengzhou University, Zhengzhou 450001, China, China |
| 2. | Dept. of Math., Dresden University of Technology, Dresden 01062, Germany |
References:
| [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. |
| [2] |
T. R. Ding, "Applications of Qualitative Methods of Ordinary Differential Equations," Higher Education Press, BeiJing, 2004. |
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T. R. Ding, A boundary value problem for the periodic Brillouin focusing system, Acta Sci. Natru. Univ. Pekinensis, 11 (1965), 31-38. |
| [4] |
Weigao Ge, "Boundary Value Problems for Nonlinear Ordinary Differential Equations," Science Press, 2007. |
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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. |
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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. |
| [7] |
Y. Ye and X. Wang, Nonlinear differential equations in electron beam focusing theory, Acta Math. Appl. Sinica, 1 (1978), 13-41. |
| [8] |
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. |
| [9] |
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. |
show all references
References:
| [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. |
| [2] |
T. R. Ding, "Applications of Qualitative Methods of Ordinary Differential Equations," Higher Education Press, BeiJing, 2004. |
| [3] |
T. R. Ding, A boundary value problem for the periodic Brillouin focusing system, Acta Sci. Natru. Univ. Pekinensis, 11 (1965), 31-38. |
| [4] |
Weigao Ge, "Boundary Value Problems for Nonlinear Ordinary Differential Equations," Science Press, 2007. |
| [5] |
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. |
| [6] |
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. |
| [7] |
Y. Ye and X. Wang, Nonlinear differential equations in electron beam focusing theory, Acta Math. Appl. Sinica, 1 (1978), 13-41. |
| [8] |
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. |
| [9] |
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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