[1]佘志炜,王全义.一类具有偏差变元的二阶泛函微分方程周期解[J].华侨大学学报(自然科学版),2009,30(6):709-714.[doi:10.11830/ISSN.1000-5013.2009.06.0709]
　SHE Zhi-wei,WANG Quan-yi.Periodic Solutions for a Class of Second Order Functional Differential Equations with a Deviating Argument[J].Journal of Huaqiao University(Natural Science),2009,30(6):709-714.[doi:10.11830/ISSN.1000-5013.2009.06.0709]
点击复制

一类具有偏差变元的二阶泛函微分方程周期解()
分享到：

《华侨大学学报（自然科学版）》[ISSN:1000-5013/CN:35-1079/N]

卷:
第30卷
期数:
2009年第6期
页码:
709-714
栏目:
出版日期:
2009-11-20

文章信息/Info

Title:
Periodic Solutions for a Class of Second Order Functional Differential Equations with a Deviating Argument
文章编号:
1000-5013(2009)06-0709-06
作者:
佘志炜; 王全义
华侨大学数学科学学院
Author(s):
SHE Zhi-wei;  WANG Quan-yi
School of Mathematical Sciences, Huaqiao University, Quanzhou 362021, China
关键词:
泛函微分方程;  周期解;  重合度;  偏差变元
Keywords:
functional differential equation;  periodic solution;  coincidence degree;  deviating argument
分类号:
O175.14
DOI:
10.11830/ISSN.1000-5013.2009.06.0709
文献标志码:
A
摘要:
利用重合度理论,研究一类具有偏差变元的二阶微分方程x″+f(t,x′(t))+g(t,x(t-τ(t)))=p(t)的周期解的存在性问题.其中,f,g∈C(R×R,R),且对任意的x∈R,g(t+ω,x)=g(t,x),p∈C(R,R),τ∈C(R,R)是ω-周期的.在不要求对所有的y∈R,函数f(t,y)≤0(f(t,y)≥0),t∈R的情况下,得到该类方程至少存在一个ω-周期解的充分条件.
Abstract:
In this paper,by means of Mawhin’s continuation theorem,we study the problem on the existence of periodic solutions for the second order differential equations with a deviating argument x″+f(t,x′(t))+g(t,x(t-τ(t)))=p(t),where f,g∈C(R×R,R); and for any x∈R,g(t+ω,x)=g(t,x),p∈C(R,R); and τ∈C(R,R) are ω-periodic.Without the condition f(t,y)≤0(f(t,y)≥0) for all y∈R and t∈R,we obtain some sufficient conditions on the existence of at least one periodic solution for this equation.

参考文献/References:

[1] 鲁世平, 葛渭高. 共振情形m-点边值问题解的存在性 [J]. 数学学报, 2006(3):687-692.
[2] POURNAKI M R, RAZANI A. On the existence of periodic solutions for a class of generalized forced Liénard equations [J]. Applied Mathematics Letters, 2007(3):248-254.
[3] WANG Wei-bing, LUO Zhi-guo. Positive periodic solutions of second-order differential equations [J]. Applied Mathematics Letters, 2007(3):266-271.
[4] ZHU Yan-ling, LU Shi-ping. Periodic solutions for p-Laplacian neutral functional differential equation with multiple deviating arguments [J]. Journal of Mathematical Analysis and Applications, 2007(2):1357-1367.doi:10.1016/j.jmaa.2007.02.085.
[5] DING Wei, HAN Mao-an, YAN Ju-rang. Periodic boundary value problems for the second order functional differential equations [J]. Journal of Mathematical Analysis and Applications, 2004(1):341-351.doi:10.1016/j.jmaa.2004.05.019.
[6] Li Yong-xiang. Positive periodic solutions of first and second order ordinary differential equations [J]. Chinese Ann Math (B), 2004(3):413-420.doi:10.1142/S025295990400038X.
[7] LIU Bing-wen, HUANG Li-hong. Periodic solutions for a kind of Rayleigh equation with a deviating argument [J]. Journal of Mathematical Analysis and Applications, 2006(2):491-500.doi:10.1016/j.jmaa.2005.08.070.
[8] 汪东树, 王全义. 一类具有时滞和比率的扩散系统正周期解 [J]. 华侨大学学报(自然科学版), 2006(4):358-361.doi:10.3969/j.issn.1000-5013.2006.04.006.
[9] GAINES R E, MAWHIN J L. Coincidence degree and nonlinear differential equation [M]. Beilin:Springer-Verlag, 1977.40-60.

相似文献/References:

[1]王全义.一类周期微分系统的同期解[J].华侨大学学报(自然科学版),1993,14(1):12.[doi:10.11830/ISSN.1000-5013.1993.01.0012]
　Wang Quanyi.Periodic Solutions for a Class of Periodic Differential Systems[J].Journal of Huaqiao University(Natural Science),1993,14(6):12.[doi:10.11830/ISSN.1000-5013.1993.01.0012]
[2]王全义.纯量Volterra积分微分方程的周期解[J].华侨大学学报(自然科学版),1994,15(2):127.[doi:10.11830/ISSN.1000-5013.1994.02.0127]
　Wang Quanyi.Periodic Solution of a Scalar Volterra Integrodifferential Equation[J].Journal of Huaqiao University(Natural Science),1994,15(6):127.[doi:10.11830/ISSN.1000-5013.1994.02.0127]
[3]王全义.一类高维周期系统的周期解[J].华侨大学学报(自然科学版),1994,15(4):363.[doi:10.11830/ISSN.1000-5013.1994.04.0363]
　Wang Quanyi.Periodic Solutions to One Class of Higher Dimensional Periodic Systems[J].Journal of Huaqiao University(Natural Science),1994,15(6):363.[doi:10.11830/ISSN.1000-5013.1994.04.0363]
[4]王全义.非线性周期系统的不稳定周期解[J].华侨大学学报(自然科学版),1995,16(2):121.[doi:10.11830/ISSN.1000-5013.1995.02.0121]
　Wang Quanyi.Unstable Periodic Solutions of Nonlinear Periodic Systems[J].Journal of Huaqiao University(Natural Science),1995,16(6):121.[doi:10.11830/ISSN.1000-5013.1995.02.0121]
[5]王全义.纯量微分积分方程的周期解[J].华侨大学学报(自然科学版),1995,16(4):353.[doi:10.11830/ISSN.1000-5013.1995.04.0353]
　Wang Quanyi.Periodic Solutions of Scalar Integrodifferential Equations[J].Journal of Huaqiao University(Natural Science),1995,16(6):353.[doi:10.11830/ISSN.1000-5013.1995.04.0353]
[6]王全义.具有无限时滞的微积分方程的周期解的存在性与唯一性[J].华侨大学学报(自然科学版),1996,17(4):336.[doi:10.11830/ISSN.1000-5013.1996.04.0336]
　Wang Quanyi.Existence and Uniqueness of Periodic Solution to the Integro-Differential Equation with infinite Time-Lag[J].Journal of Huaqiao University(Natural Science),1996,17(6):336.[doi:10.11830/ISSN.1000-5013.1996.04.0336]
[7]王全义.一个造血模型周期解的存在性及唯一性[J].华侨大学学报(自然科学版),1997,18(1):11.[doi:10.11830/ISSN.1000-5013.1997.01.0011]
　Wang Quanyi.Existence and Uniqueness of Periodic Solution to a Hematopoiesis Model[J].Journal of Huaqiao University(Natural Science),1997,18(6):11.[doi:10.11830/ISSN.1000-5013.1997.01.0011]
[8]王全义.一个造血模型周期解的稳定性[J].华侨大学学报(自然科学版),1997,18(3):219.[doi:10.11830/ISSN.1000-5013.1997.03.0219]
　Wang Quanyi.Stability of Periodic Solution to a Hematopoiesis Model[J].Journal of Huaqiao University(Natural Science),1997,18(6):219.[doi:10.11830/ISSN.1000-5013.1997.03.0219]
[9]王全义.线性微分积分方程的周期解[J].华侨大学学报(自然科学版),2001,22(2):117.[doi:10.3969/j.issn.1000-5013.2001.02.002]
　Wang Quanyi.Periodic Solution to Integrodifferential Equation[J].Journal of Huaqiao University(Natural Science),2001,22(6):117.[doi:10.3969/j.issn.1000-5013.2001.02.002]
[10]王全义.线性积分微分方程的周期解的存在唯一性[J].华侨大学学报(自然科学版),2002,23(2):111.[doi:10.3969/j.issn.1000-5013.2002.02.001]
　Wang Quanyi.Existence and Uniqueness of Periodic Solutions to Linear Integrodifferential Equations[J].Journal of Huaqiao University(Natural Science),2002,23(6):111.[doi:10.3969/j.issn.1000-5013.2002.02.001]
[11]王全义.具状态依赖时滞的泛函微分方程周期解[J].华侨大学学报(自然科学版),2007,28(2):212.[doi:10.3969/j.issn.1000-5013.2007.02.026]
　WANG Quan-yi.Periodic Solutions for Functional Differential Equations with State-Dependent Delay[J].Journal of Huaqiao University(Natural Science),2007,28(6):212.[doi:10.3969/j.issn.1000-5013.2007.02.026]
[12]曹君艳,王全义.一类具多时滞二阶非线性微分方程的周期解[J].华侨大学学报(自然科学版),2012,33(3):348.[doi:10.11830/ISSN.1000-5013.2012.03.0348]
　CAO Jun-yan,WANG Quan-yi.Periodic Solutions for Second-Order Differential Equations with Deviating Arguments[J].Journal of Huaqiao University(Natural Science),2012,33(6):348.[doi:10.11830/ISSN.1000-5013.2012.03.0348]
[13]佘志炜,王全义.一类一阶泛函微分方程非平凡周期解的存在性[J].华侨大学学报(自然科学版),2013,34(4):460.[doi:10.11830/ISSN.1000-5013.2013.04.0460]
　SHE Zhi-wei,WANG Quan-yi.Existence of Nontrivial Periodic Solutions for a Class of First Order Nonlinear Functional Differential Equations[J].Journal of Huaqiao University(Natural Science),2013,34(6):460.[doi:10.11830/ISSN.1000-5013.2013.04.0460]

备注/Memo

备注/Memo:
福建省自然科学基金资助项目(Z0511026)
更新日期/Last Update: 2014-03-23