| 非线性微分系统解的有界性和周期解的存在性 |
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| 引用本文： | 颜跃新,周正新.非线性微分系统解的有界性和周期解的存在性[J].数学研究及应用,2002,22(3):441-446. |
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| 作者姓名： | 颜跃新 周正新 |
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| 作者单位： | 扬州大学理学院数学系,江苏,扬州,225002 |
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| 基金项目： | 江苏省教委计划指导性项目(99KJD110005) |
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| 摘 要： | 本文运用了比较新的手法,证明了非线性微分系统(dx)/(dt)=1/(a(x))c(y)-b(x)];(dy)/(dt)=-a(x)h(x)-e(t)](1)(其中a(x),b(x),h(x),c(y),e(t)为连续可微函数,x,y∈R,t∈0,+∞),且a(x)>0)解的有界性及周期解的存在性,并应用该结论讨论了强迫振动方程:x+(f(x)+g(x)x)x+h(x)=e(t)(2)(其中f(x),g(x)为连续可微函数,x∈R,h(x),e(t)同上)解的有界性及周期解的存在性.
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| 关 键 词： | 非线性 有界性 周期解 |
| 文章编号： | 1000-341X(2002)03-0441-06 |
| 收稿时间： | 1999/7/15 0:00:00 |
| 修稿时间： | 1999年7月15日 |
Boundedness of Solutions and Existence of Periodic Solutions of Nonlinear Differential Equations |
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| YAN Yue-xin and ZHOU Zheng-xin.Boundedness of Solutions and Existence of Periodic Solutions of Nonlinear Differential Equations[J].Journal of Mathematical Research with Applications,2002,22(3):441-446. |
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| Authors: | YAN Yue-xin and ZHOU Zheng-xin |
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| Institution: | Dept. of Math.; College of Science; Yangzhou University; Jiangsu; China;Dept. of Math.; College of Science; Yangzhou University; Jiangsu; China |
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| Abstract: | In this paper, we used a new method to discuss the boundedness and existence of periodic solutions of nonlinear differential system (dx)/(dt)=1/(a(x))c(y)-b(x)];(dy)/(dt)=-a(x)h(x)-e(t)] and applied these conclusions to study the boundedness of solutions and the existence of periodic solutions of the forcing vibrating differential equations x+(f(x)+g(x)x)x+h(x)=e(t). |
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| Keywords: | Nonlinear boundedness periodic solution |
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