具有一般非线性弹性力和广义阻尼力的相对转动非线性系统的周期解问题

李晓静; 严静; 陈绚青; 曹毅

doi:10.7498/aps.63.200202

摘要

讨论了一类相对转动非线性动力系统的周期解问题. 首先建立了一类具有一般非线性弹性力、广义阻尼力和强迫周期力项的相对转动非线性动力系统；其次得到了对应自治系统的周期解不存在性结果，以及运用Mawhin重合度理论得到了该模型的周期解存在性结果，推广了已有的结果；最后举例证明本文结果的正确性.

关键词:

The periodic solution problem of a relative rotation nonlinear system is considered. Firstly, the relative rotation nonlinear dynamic system is established, which contains nonlinear elastic force, commonly damped force and forcing periodic force. Secondly, the result about the nonexistence of periodic solution of the corresponding autonomous system is obtained, and some results about the existence of periodic solutions of the system are obtained by using the continuation theorem of coincidence degree theory. The significance is that we generalize the existing results of the literature. Finally an example is given to illustrate that our results are right.

Keywords:

作者及机构信息

1.
江苏理工学院数理学院, 常州 213001

基金项目: 国家自然科学基金（批准号：51277017，11202106）、江苏省自然科学基金（批准号：BK2012583，13KJB170016）和江苏理工学院青年基金（批准号：KYY13032）资助的课题.

Authors and contacts

1.
College of Mathematics and Physics, Jiangsu University of Technology, Changzhou 213001, China

Funds: Project supported by the National Natural Science Foundation of China (Grant Nos. 51277017, 11202106), the Natural Science Foundation of Jiangsu Province, China (Grant Nos. BK2012583, 13KJB170016), and the Young Scientists Foundation of Jiangsu University of Technology, China (Grant No. KYY 13032).

参考文献

[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, Chen X W, Fu J L 2001 Chin. Phys. 10 271
[6]	Luo S K 2002 Chin. Phys. Lett. 19 449
[7]	Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 429
[8]	Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 523
[9]	Wang Y Z, Zhou Y Z 2011 Chin. Phys. B 20 040501
[10]	Wang K, Guan X P, Ding X F, Qiao J M 2010 Acta Phys. Sin. 59 6859 (in Chinese) [王坤, 关新平, 丁喜峰, 乔杰敏 2010 物理学报 59 6859]
[11]	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]
[12]	Li X J, Chen X Q 2012 Acta Phys. Sin. 61 210201 (in Chinese) [李晓静, 陈绚青 2012 物理学报 61 210201]
[13]	Wang K, Zhu Y L 2010 Neurocomputing 73 3300
[14]	Wang K 2011 Nonlinear Analysis: Real World Application 12 1062
[15]	Wang X L, Du Z J, Liang J 2010 Nonlinear Analysis: Real World Application 11 4054
[16]	Peng S G 2007 Nonlinear Analysis 67 138
[17]	Xiao B, Liu B W 2009 Nonlinear Analysis 10 16
[18]	Tang Y, Li Y Q 2008 J. Math. Anal. Appl. 340 1380
[19]	Gao H, Liu B W 2009 Applied Mathematics and Computation 211 148
[20]	Li X J 2007 Chin. Phys. 16 2837
[21]	Li X J 2008 Chin. Phys. B 17 1946
[22]	Li X J 2010 Chin. Phys. B 19 020202
[23]	Li X J 2010 Chin. Phys. B 19 030201
[24]	Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[25]	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)]
[26]	Li X J 2009 Nonlinear Analysis 71 2764

施引文献

[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, Chen X W, Fu J L 2001 Chin. Phys. 10 271
[6]	Luo S K 2002 Chin. Phys. Lett. 19 449
[7]	Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 429
[8]	Luo S K, Chen X W, Guo Y X 2002 Chin. Phys. 11 523
[9]	Wang Y Z, Zhou Y Z 2011 Chin. Phys. B 20 040501
[10]	Wang K, Guan X P, Ding X F, Qiao J M 2010 Acta Phys. Sin. 59 6859 (in Chinese) [王坤, 关新平, 丁喜峰, 乔杰敏 2010 物理学报 59 6859]
[11]	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]
[12]	Li X J, Chen X Q 2012 Acta Phys. Sin. 61 210201 (in Chinese) [李晓静, 陈绚青 2012 物理学报 61 210201]
[13]	Wang K, Zhu Y L 2010 Neurocomputing 73 3300
[14]	Wang K 2011 Nonlinear Analysis: Real World Application 12 1062
[15]	Wang X L, Du Z J, Liang J 2010 Nonlinear Analysis: Real World Application 11 4054
[16]	Peng S G 2007 Nonlinear Analysis 67 138
[17]	Xiao B, Liu B W 2009 Nonlinear Analysis 10 16
[18]	Tang Y, Li Y Q 2008 J. Math. Anal. Appl. 340 1380
[19]	Gao H, Liu B W 2009 Applied Mathematics and Computation 211 148
[20]	Li X J 2007 Chin. Phys. 16 2837
[21]	Li X J 2008 Chin. Phys. B 17 1946
[22]	Li X J 2010 Chin. Phys. B 19 020202
[23]	Li X J 2010 Chin. Phys. B 19 030201
[24]	Gaines R E, Mawhin J L 1977 Coincidence Degree and Nonlinear Differential Equations (Berlin: Springer)
[25]	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)]
[26]	Li X J 2009 Nonlinear Analysis 71 2764

计量

文章访问数: 5055
PDF下载量: 474
被引次数: 0

姓名
邮箱
手机号码
标题
留言内容
验证码

搜索

留言板