| 一类二阶泛函微分方程的多重周期解 |
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| 引用本文： | 郑冬梅,鲁世平.一类二阶泛函微分方程的多重周期解[J].系统科学与数学,2010,30(3):370-378. |
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| 作者姓名： | 郑冬梅 鲁世平 |
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| 作者单位： | 1. 安徽师范大学数学系,芜湖,241000;安徽师范大学附属中学,芜湖,241000
2. 安徽师范大学数学系,芜湖,241000 |
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| 基金项目： | 国家自然科学基金，安徽省自然科学基金，安徽省教育厅重点基金，安徽省高等学校优秀青年人才基金 |
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| 摘 要： | 利用变分原理和Z_2不变群指标,得出二阶泛函微分方程x″(t-τ)+c(x(t)-x(t-2τ))′-x(t-τ)+λf(t,x(t),x(t-τ),x(t-2τ))=0的多重周期解的存在性质.
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| 关 键 词： | 变分原理 $Z_{2}$不变群指标 临界点 P.S.条件 多重周期解. |
| 收稿时间： | 2008-10-27 |
| 修稿时间： | 2009-8-24 |
MULTIPLE PERIODIC SOLUTIONS TO A CLASS OF SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS |
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| ZHENG Dongmei,LU Shiping.MULTIPLE PERIODIC SOLUTIONS TO A CLASS OF SECOND-ORDER FUNCTIONAL DIFFERENTIAL EQUATIONS[J].Journal of Systems Science and Mathematical Sciences,2010,30(3):370-378. |
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| Authors: | ZHENG Dongmei LU Shiping |
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| Institution: | (1)Department of Mathematics, Anhui Normal University, Wuhu 241000; The High School Affiliated to Anhui Normal University, Wuhu 241000;(2)Department of Mathematics, Anhui Normal University, Wuhu 241000 |
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| Abstract: | By means of variational principle and $Z_{2}$ group index theory, we obtain the existence of multiple periodic solutions to second-order functional differential equations $x'(t-\tau)+c(x(t)-x(t-2\tau))'-x(t-\tau)+\lambda f(t,x(t),x(t-\tau),x(t-2\tau))=0$. |
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| Keywords: | Variational structure $Z_{2}$ group index theory critical point the Palais-Smale condition multiple periodic solutions |
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