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Existence of periodic solutions for the nonlinear functional differential equation in the lossless transmission line model |
Wang Na(汪娜)† |
Department of Mathematics, East China Normal University, Shanghai 200241, China |
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Abstract We study a time delay equation for the lossless transmission line model. Under suitable conditions, by using the continuation theorem of the coincidence degree theory, the existence of the periodic solution for the nonlinear functional differential equation is obtained.
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Received: 11 July 2011
Revised: 01 September 2011
Accepted manuscript online:
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PACS:
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02.30.Hq
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(Ordinary differential equations)
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02.30.Ks
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(Delay and functional equations)
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02.30.Sa
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(Functional analysis)
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02.30.Tb
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(Operator theory)
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Fund: Project supported by the National Natural Science Foundation of China (Grant No. 11071075). |
Cite this article:
Wang Na(汪娜) Existence of periodic solutions for the nonlinear functional differential equation in the lossless transmission line model 2012 Chin. Phys. B 21 010202
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[1] |
Kuang Y 1993 Delay Differential Equations with Applications in Population Dynamical System (New York: Academic Press)
|
[2] |
Komanovskii V B and Nosov V R 1986 Stability of Functional Differential Equations (London: Academic Press)
|
[3] |
Mo J Q 1993 J. Math. Anal. Appl. 178 289
|
[4] |
Mo J Q 1989 Sci. China Ser. A 32 1306
|
[5] |
Mo J Q and Lin W T 2005 Acta Math. Appl. Sin. 21 101 (in Chinese)
|
[6] |
Mo J Q, Zhang W J and He M 2007 Acta Math. Sci. 27 777
|
[7] |
Mo J Q, Zhu J and Wang H 2003 Prog. Nat. Sci. 13 768
|
[8] |
Mo J Q 2009 Chin. Phys. Lett. 26 010204
|
[9] |
Mo J Q 2009 Acta Phys. Sin. 58 693 (in Chinese)
|
[10] |
Mo J Q 2009 Acta Phys. Sin. 58 2930 (in Chinese)
|
[11] |
Mo J Q, Lin W T and Wang H 2007 Prog. Nat. Sci. 17 230
|
[12] |
Mo J Q and Lin W T 2008 Chin. Phys. B 17 370
|
[13] |
Mo J Q and Lin W T 2008 Chin. Phys. B 17 743
|
[14] |
Lu S P and Ge W G 2003 Nonlinear Analysis 54 1285
|
[15] |
Liu B W and Hang L H 2006 Acta Math. Sin. (Chin. Series) 49 1347 (in Chinese)
|
[16] |
Liu B W and Huang L H 2006 J. Math. Anal. Appl. 322 121
|
[17] |
Liu X P, Jia M and Ren R 2007 Math. Sci. Acta A 27A 037 (in Chinese)
|
[18] |
Zhang L S, Cai L and Feng C W 2011 Acta Phys. Sin. 60 030308 (in Chinese)
|
[19] |
Wang N and Ni M K 2011 Acta Phys. Sin. 60 050203 (in Chinese)
|
[20] |
Hale J 1977 Theory of Functional Differential Equations (New York: Springer)
|
[21] |
Gaines R E and Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
|
[22] |
Lu S P and Ge W G 2005 J. Sys. Sci. Math. Scis. 25 216 (in Chinese)
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