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The periodic problem of the corresponding autonomous system is discussed. Some results on the existence and uniqueness of periodic solutions of the system are obtained by using the continuation theorem of coincidence degree theory. The results available from the literature are generalized. Furthermore, an example is given to illustrate our results are new.
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Keywords:
- relative rotation /
- nonlinear dynamic system /
- periodic solution /
- existence and uniqueness
[1] Carmeli M 1985 Found. Phys. 15 175
[2] Carmeli M 1986 Int. J. Theor. Phys. 15 89
[3] Luo S K 1996 J. Beijing Inst. Technol. 16(S1) 154 (in Chinese) [罗绍凯 1996 北京理工大学学报 16(S1) 154]
[4] Luo S K 1998 Appl. Math. Mech. 19 45
[5] Luo S K, Fu J L, Chen X W 2001 Acta Phys. Sin. 50 383 (in Chinese) [罗绍凯, 傅景礼, 陈向炜 2001 物理学报 50 383]
[6] Fu J L, Chen L Q, Xue Y 2003 Acta Phys. Sin. 52 256 (in Chinese) [傅景礼, 陈立群, 薛云 2003 物理学报 52 256]
[7] Zhang K, Feng J 2005 Acta Phys. Sin. 54 2985 (in Chinese) [张凯, 冯俊 2005 物理学报 54 2985]
[8] Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004 物理学报 53 5]
[9] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯 2002 物理学报 51 712]
[10] Luo S K 2002 Acta Phys. Sin. 51 1416 (in Chinese) [罗绍凯 2002 物理学报 51 1416]
[11] Luo S K, Chen X W, Fu J L 2001 Chin. Phys. 10 271
[12] Luo S K 2002 Chin. Phys. Lett. 19 449
[13] Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 429
[14] Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 523
[15] Dong Q L, Liu B 2002 Acta Phys. Sin. 51 2191 (in Chinese) [董全林, 刘彬 2002 物理学报 51 2191]
[16] Dong Q L, Wang K, Zhang C X, Liu B 2004 Acta Phys. Sin. 53 337 (in Chinese) [董全林, 王坤, 张春熹, 刘彬 2004 物理学报 53 337]
[17] Wang K 2005 Acta Phys. Sin. 54 5530 (in Chinese) [王坤 2005 物理学报 54 5530]
[18] Wang K 2005 Acta Phys. Sin. 54 3987 (in Chinese) [王坤 2005 物理学报 54 3987]
[19] Zhao W, Liu B 2005 Acta Phys. Sin. 54 4543 (in Chinese) [赵武, 刘彬 2005 物理学报 54 4543]
[20] Zhao W, Liu B, Shi P M, Jiang J S 2006 Acta Phys. Sin. 55 3852 (in Chinese) [赵武, 刘彬, 时培明, 蒋金水 2006 物理学报 55 3852]
[21] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [ 时培明, 刘彬 2007 物理学报 56 3678]
[22] Wang K, Guan X P, Qiao J M 2010 Acta Phys. Sin. 59 3648 (in Chinese) [王坤, 关新平, 乔杰敏 2010 物理学报 59 3648]
[23] Mo J Q, Cheng R J, Ge H X 2011 Acta Phys. Sin. 60 040203 (in Chinese) [莫嘉琪, 程荣军, 葛红霞 2011 物理学报 60 040203]
[24] Li X J 2007 Chin. Phys. 16 2837
[25] Li X J 2008 Chin. Phys. B 17 1946
[26] Li X J 2008 Acta Phys. Sin. 57 5366 (in Chinese) [李晓静 2008 物理学报 57 5366]
[27] Li X J 2010 Chin. Phys. B 19 020202
[28] Li X J 2010 Chin. Phys. B 19 030201
[29] Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[30] Zhang J Y, Feng B Y 2000 The Geometric Theory and Bifurcation Problem of Ordinary Differential Equations (Beijing: Peking University Press) (in Chinese) [张锦炎, 冯贝叶 2000 常微分方程几何理论与分支问题 (北京: 北京大学出版社)]
[31] Li X J 2009 Nonlinear Analysis 71 2764
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[1] Carmeli M 1985 Found. Phys. 15 175
[2] Carmeli M 1986 Int. J. Theor. Phys. 15 89
[3] Luo S K 1996 J. Beijing Inst. Technol. 16(S1) 154 (in Chinese) [罗绍凯 1996 北京理工大学学报 16(S1) 154]
[4] Luo S K 1998 Appl. Math. Mech. 19 45
[5] Luo S K, Fu J L, Chen X W 2001 Acta Phys. Sin. 50 383 (in Chinese) [罗绍凯, 傅景礼, 陈向炜 2001 物理学报 50 383]
[6] Fu J L, Chen L Q, Xue Y 2003 Acta Phys. Sin. 52 256 (in Chinese) [傅景礼, 陈立群, 薛云 2003 物理学报 52 256]
[7] Zhang K, Feng J 2005 Acta Phys. Sin. 54 2985 (in Chinese) [张凯, 冯俊 2005 物理学报 54 2985]
[8] Luo S K 2004 Acta Phys. Sin. 53 5 (in Chinese) [罗绍凯 2004 物理学报 53 5]
[9] Luo S K 2002 Acta Phys. Sin. 51 712 (in Chinese) [罗绍凯 2002 物理学报 51 712]
[10] Luo S K 2002 Acta Phys. Sin. 51 1416 (in Chinese) [罗绍凯 2002 物理学报 51 1416]
[11] Luo S K, Chen X W, Fu J L 2001 Chin. Phys. 10 271
[12] Luo S K 2002 Chin. Phys. Lett. 19 449
[13] Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 429
[14] Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 523
[15] Dong Q L, Liu B 2002 Acta Phys. Sin. 51 2191 (in Chinese) [董全林, 刘彬 2002 物理学报 51 2191]
[16] Dong Q L, Wang K, Zhang C X, Liu B 2004 Acta Phys. Sin. 53 337 (in Chinese) [董全林, 王坤, 张春熹, 刘彬 2004 物理学报 53 337]
[17] Wang K 2005 Acta Phys. Sin. 54 5530 (in Chinese) [王坤 2005 物理学报 54 5530]
[18] Wang K 2005 Acta Phys. Sin. 54 3987 (in Chinese) [王坤 2005 物理学报 54 3987]
[19] Zhao W, Liu B 2005 Acta Phys. Sin. 54 4543 (in Chinese) [赵武, 刘彬 2005 物理学报 54 4543]
[20] Zhao W, Liu B, Shi P M, Jiang J S 2006 Acta Phys. Sin. 55 3852 (in Chinese) [赵武, 刘彬, 时培明, 蒋金水 2006 物理学报 55 3852]
[21] Shi P M, Liu B 2007 Acta Phys. Sin. 56 3678 (in Chinese) [ 时培明, 刘彬 2007 物理学报 56 3678]
[22] Wang K, Guan X P, Qiao J M 2010 Acta Phys. Sin. 59 3648 (in Chinese) [王坤, 关新平, 乔杰敏 2010 物理学报 59 3648]
[23] Mo J Q, Cheng R J, Ge H X 2011 Acta Phys. Sin. 60 040203 (in Chinese) [莫嘉琪, 程荣军, 葛红霞 2011 物理学报 60 040203]
[24] Li X J 2007 Chin. Phys. 16 2837
[25] Li X J 2008 Chin. Phys. B 17 1946
[26] Li X J 2008 Acta Phys. Sin. 57 5366 (in Chinese) [李晓静 2008 物理学报 57 5366]
[27] Li X J 2010 Chin. Phys. B 19 020202
[28] Li X J 2010 Chin. Phys. B 19 030201
[29] Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[30] Zhang J Y, Feng B Y 2000 The Geometric Theory and Bifurcation Problem of Ordinary Differential Equations (Beijing: Peking University Press) (in Chinese) [张锦炎, 冯贝叶 2000 常微分方程几何理论与分支问题 (北京: 北京大学出版社)]
[31] Li X J 2009 Nonlinear Analysis 71 2764
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