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高维次线性时滞差分方程周期解的存在性 被引量：2

The existence of periodic solutions to higher-order dimensional sublinear delay difference equation
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摘要 应用临界点理论,研究如下高维次线性时滞差分方程Δx(n)=-f(x(n-T))的周期解的存在性,其中f∈C(Rm,Rm),x∈Rm,T为给定的正整数.当f(x)满足次线性增长条件时,得到了上述方程以(4T+2)为周期的周期解存在性的若干充分条件. By using critical point theory , the existence of periodic solutions to following higher-order dimension-al sublinear delay difference equation is investigated Δx（n）=-f（x（n-T））,where f∈C（Rm,Rm）,x∈Rm and T is a given positive integer .When f（u） grows sublinearly , some sufficient conditions are obtained for the existence of periodic solutions with period 4T＋2 to the above equation .
作者 郭志明 郭丽芬
机构地区 广州大学数学与信息科学学院
出处 《广州大学学报（自然科学版）》 CAS 2014年第3期7-12,共6页 Journal of Guangzhou University:Natural Science Edition
基金 国家自然科学基金资助项目(11371107) 教育部博士点基金资助项目(20124410110001)
关键词 次线性增长 时滞差分方程 周期解 临界点 鞍点定理 sublinear growth delay difference equation periodic solution critical point Saddle point theorem
分类号 O175.7 [理学—基础数学]
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参考文献2

二级参考文献12

  • 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.
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共引文献5

同被引文献15

  • 1KAPLAN J L, YORKE J A. Ordinary differential equations which yield periodic solution of delay equations [ J ]. J Math Anal Appl, 1974, 48: 317-324.
  • 2温立志.-类微分差分方程的周期解的存在性[J].科学通报,1986,22:1755.
  • 3CHEN Y. The existence of periodic solutions of the equation (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 Hamihonian systems [J]. Nonl Anal TMA, 1998, 31 : 45-54.
  • 7GUO Z M, YU J S. Multiplicity results for periodic solutions to delay differential equations via critical point theory[ J]. J Diff Equ, 2005, 218 : 15-35.
  • 8GUO C J, GUO Z M. Existence of multiple periodic solutions for a class of second-order delay differential equations [ J ]. Nonl Anal: Real W Appl, 2009, 10(5) : 3285-3297.
  • 9GUO Z M, YU J S. Multiplicity results on period solutions to higher dimensional differential equations with multiple delays [J]. JDynaDiffEqua, 2011, 23(4): 1029-1052.
  • 10YU J S. A note on periodic solutions of the delay differential equation x' (t) = -f( x ( t - 1 ) ) [ J ]. Pro Amer Math Soci, 2013, 141: 1281-1288.

引证文献2

广州大学学报（自然科学版）
2014年 第3期

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