一类二阶泛函微分方程的多重周期解

郑冬梅;鲁世平

系统科学与数学 ›› 2010, Vol. 30 ›› Issue (3) : 370-378.

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系统科学与数学 ›› 2010, Vol. 30 ›› Issue (3) : 370-378. DOI: 10.12341/jssms08952
论文

一类二阶泛函微分方程的多重周期解

    郑冬梅(1), 鲁世平(2)
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Multiple Periodic Solutions to a Class of Second-Order Functional Differential Equations

    ZHENG Dongmei (1), LU Shiping(2)
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摘要

利用变分原理和Z2 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.

Abstract

By means of variational principle and Z2 group index theory, we obtain the existence of multiple periodic solutions to second-order functional differential equations x″(t−τ)+c(x(t)−x(t−2τ))′−x(t−τ)+λf(t,x(t),x(t−τ),x(t−2τ))=0.

关键词

变分原理 / Z2不变群指标 / 临界点 / P.S.条件 / 多重周期解.

Key words

Variational structure / Z2 group index theory / critical point / the Palais-Smale condition / multiple periodic solutions.

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郑冬梅 , 鲁世平. 一类二阶泛函微分方程的多重周期解. 系统科学与数学, 2010, 30(3): 370-378. https://doi.org/10.12341/jssms08952
ZHENG Dongmei , LU Shiping. Multiple Periodic Solutions to a Class of Second-Order Functional Differential Equations. Journal of Systems Science and Mathematical Sciences, 2010, 30(3): 370-378 https://doi.org/10.12341/jssms08952
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