| 一类二阶微分方程的无穷周期解 |
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| 引用本文： | 甘丽丽,鲁世平.一类二阶微分方程的无穷周期解[J].安徽师范大学学报(自然科学版),2010,33(1):5-10. |
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| 作者姓名： | 甘丽丽 鲁世平 |
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| 作者单位： | 安徽师范大学数学计算机科学学院,安徽,芜湖,241000;安徽师范大学数学计算机科学学院,安徽,芜湖,241000 |
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| 基金项目： | Sponsored by the key NSF of Education Ministry of China |
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| 摘 要： | 通过临界点理论和Z2不变群指标理论,证得I(x)有无穷多个临界点,再由变分原理可得方程(2)与方程(3)等价,在改变条件的情况下,得出了一在二阶泛函微分方程存在无穷多个周期解.
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| 关 键 词： | 变分结构 Z2不变指标群理论 临界点 周期解 |
Infinite Periodic Solutions to a Class of Second-Order Differential Equations |
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| GAN Li-li,LU Shi-ping.Infinite Periodic Solutions to a Class of Second-Order Differential Equations[J].Journal of Anhui Normal University(Natural Science Edition),2010,33(1):5-10. |
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| Authors: | GAN Li-li LU Shi-ping |
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| Abstract: | By critical point and Z2-group index theory, the functional I(x) posesses infinite critical points and equation(2)is equivalent to equation(3)by the variational structure. In the changed conditions,we obtain infinite periodic solutions to a class of second-order differential equations (c(t)x'(t-r))'+f(t,x(t),x(t-r),x(t-2r))=0. |
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| Keywords: | variational structure Z2-group index theory critical points periodic solutions |
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