| 一类二阶时滞微分方程多重周期解 |
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| 引用本文： | 陈业,鲁世平. 一类二阶时滞微分方程多重周期解[J]. 安庆师范学院学报(自然科学版), 2009, 15(1): 17-20 |
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| 作者姓名： | 陈业 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： | 教育部科学技术研究重点项目 |
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| 摘 要： | 利用变分原理和Z2不变群指标对一类二阶时滞微分方程（a（t）x′（t-τ））′-b（t）x（t-）τ＋fλ（t,x（t）,x（t-）τ,x（t-2）τ）=0的周期解问题进行研究,得出在一些条件下方程有2n个周期为2π的非平凡周期解。
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| 关 键 词： | 变分原理 Z2不变群指标 临界点 |
Multiple Periodic Solutions to a Class of Second-order Differential Equations with Delays |
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| CHE Ye,LU Shi-ping. Multiple Periodic Solutions to a Class of Second-order Differential Equations with Delays[J]. Journal of Anqing Teachers College(Natural Science Edition), 2009, 15(1): 17-20 |
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| Authors: | CHE Ye LU Shi-ping |
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| Affiliation: | (Department of Mathematics, Anhui Normal University, Wuhu 241000, China) |
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| Abstract: | By means of variational principle and Z2-group index theory,the authors study a kind of periodic solutions of the second-order differential equations with delays as the following type(a(t)x′(t-τ))′-b(t)x(t-τ)+λf(t,x(t),x(t-τ),x(t-2τ))=0We obtain that the equation has nontrivial-periodic solutions under some conditions. |
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| Keywords: | Variational structure z2-group index theory Critical points |
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