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A SURVEY ON THE PERIODIC SOLUTIONS TO KAPLAN-YORKE TYPE DELAY DIFFERENTIAL EQUATION-I 被引量：1

A SURVEY ON THE PERIODIC SOLUTIONS TO KAPLAN-YORKE TYPE DELAY DIFFERENTIAL EQUATION-I
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摘要 Since 1974, studying the original delay differential equation given by Kaplan and Yorke is about the problem on the existence of its periodic solutions, there have been a series of interesting and significant results in the previous literature. In this paper, we present a survey of some basic results. Some interesting open problems are also Since 1974, studying the original delay differential equation given by Kaplan and Yorke is about the problem on the existence of its periodic solutions, there have been a series of interesting and significant results in the previous literature. In this paper, we present a survey of some basic results. Some interesting open problems are also
作者 Jianshe Yu Zhiming Guo
机构地区 College of Math.and Information Sciences
出处 《Annals of Differential Equations》 2014年第1期97-114,共18页 微分方程年刊（英文版）
基金 partially supported by National Natural Science Foundation of China Program for Changjiang Scholars and Innovative Research Team in University(IRT1226)
关键词 delay differential equation Kaplan-Yorke conjecture periodic solu-tion Hamiltonian system delay differential equation Kaplan-Yorke conjecture periodic solu-tion Hamiltonian system
分类号 O175 [理学—基础数学]
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  • 1Kaplan J L,Yorke J A.Ordinary differential equations which yield periodic solution of delay equations [J].J Math Anal Appl,1974,48:314-324.
  • 2温立志.一类微分差分方程的周期解的存在性.科学通报,1986,22:1755-1755.
  • 3CHEN Y.The existence of periodic solutions of the equation x(t)=-f(x(t),x(t-1))[J].J Math Anal Appl,1992,163:227-237.
  • 4GE W.Existence of many and infinitely many periodic solutions for some types of differential delay equations[J].J Beijing Inst Tech,1993,1:5-14.
  • 5Gopalsamy K,LI J,HE X.On the construction of Kaplan-Yorke type for some differential delay equations [J].Appl Anal,1995,59:65-80.
  • 6LI J,HE X.Multiple periodic solutions of differential delay equations created by asymptotically linear Hamiltonian systems[J].Nonlinear Analysis TMA,1998,31:45-54.
  • 7GUO Zhiming,YU Jianshe.Multiplicity results for periodic solutions to delay differential equations via critical point theory[J].Journal of Differential Equations,2005,218:15-35.
  • 8FEI G.Multiple periodic solutions of differential delay equations via Hamiltonian systems(Ⅰ)[J].Nonlinear Analysis TMA,2006,65:25-39.
  • 9FEI G.Multiple periodic solutions of differential delay equations via Hamiltonian systems(Ⅱ)[J].Nonlinear Analysis TMA,2006,65:40-58.
  • 10GUO Zhiming,YU Jianshe.The existence of periodic and subharmonic solutions to subquadratic secondorder difference equations[J].J London Math Soc,2003,68(2):419-430.

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Annals of Differential Equations
2014年 第1期

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