您的位置：山东大学 -> 科技期刊社 -> 《山东大学学报（理学版）》

山东大学学报（理学版） ›› 2015, Vol. 50 ›› Issue (06): 69-74.doi: 10.6040/j.issn.1671-9352.0.2014.585

• 论文 • 上一篇    下一篇

带双参数的脉冲泛函微分方程正周期解的存在性

徐嫚   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 收稿日期:2014-12-26 修回日期:2015-05-20 出版日期:2015-06-20 发布日期:2015-07-31
  • 作者简介:徐嫚(1989-),女,硕士研究生,研究方向为常微分方程边值问题.E-mail:xmannwnu@126.com
  • 基金资助:
    国家自然科学基金资助项目(11361054);甘肃省自然科学基金资助项目(1208RJZA258)

Existence of positive periodic solutions of impulsive functional differential equations with two parameters

XU Man   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Received:2014-12-26 Revised:2015-05-20 Online:2015-06-20 Published:2015-07-31

PDF (PC)

555

摘要： 研究了带双参数的脉冲泛函微分方程 u'(t)=h(t,u(t))-λf(t,u(t-τ(t))), t∈R, t≠tk, u(t+k)-u(tk)=μIk(tk,u(tk-τ(tk))) 正周期解的存在性, 其中λ>0, μ≥0为参数, 获得了其在更一般条件下正周期解的存在性结果。主要结果的证明基于不动点指数理论。

关键词: 脉冲泛函微分方程, 双参数, 正周期解, 不动点指数

Abstract: We study the existence of positive periodic solutions of impulsive functional differential equations with two parameters u'(t)=h(t,u(t))-λf(t,u(t-τ(t))), t∈R, t≠tk, u(t+k)-u(tk)=μIk(tk,u(tk-τ(tk))), where λ>0, μ≥0 are parameters and show the existence results of positive periodic solutions in more general conditions. The proof of the main results is based on the fixed point index theory.

Key words: Impulsive functional differential equations, two parameters, positive periodic solutions, fixed point index

中图分类号: 

  • O175.8
[1] LI Wantong, HUO Haifeng. Existence and global attractivity of positive periodic solutions of functional differential equations with impulses[J]. Nonlinear Analysis, 2004, 59(6):857-877.
[2] CHOISY M, GUEGAN J F, ROHANI P. Dynamics of infectious diseases and pulse vaccination:teasing apart the embedded resonance effects[J]. Physica D, 2006, 223(1):26-35.
[3] DONOFRIO A. On pulse vaccination strategy in the SIR epidemic model with vertical transmission[J]. Appl Math Lett, 2005, 18(7):729-732.
[4] GAO Shujing, CHEN Lansun, NIETO J J, et al. Analysis of a delayed epidemic model with pulse vaccination and saturation incidence[J]. Vaccine, 2006, 24(35-36):6037-6045.
[5] TANG Sanyi, CHEN Lansun. Density-dependent birth rate, birth pulses and their population dynamic consequences[J]. J Math Biol, 2002, 44(2):185-199.
[6] COOKE K L, KAPLAN J L. A periodicity threshold theorem for epidemic and population growth[J]. Math Biosci, 1976, 31(1-2):87-104.
[7] GOPALSAMY K. Stability and oscillation in delay differential equations of population dynamics[J]. Dordrecht: Kluwer Academic Publishers Group, 1992.
[8] BAI Dingyong, XU Yuantong. Periodic solutions of first order functional differential equations with periodic deviations[J]. Comput Math Appl, 2007, 53(9):1361-1366.
[9] LIU Xilan, LI Wantong. Existence and uniqueness of positive periodic solutions of functional differential equations[J]. J Math Anal Appl, 2004, 293(1):28-39.
[10] WANG Haiyan. Positive periodic solutions of functional differential equations[J]. Journal Differential Equations, 2004, 202(2):354-366.
[11] WU Yuexiang. Existence of positive periodic solutions for a functional differential equations with a parameter[J]. Nonlinear Analysis, 2008, 68(7):1954-1962.
[12] JIN Zhilong, WANG Haiyan. A note on positive periodic solutions of delayed differential equations[J]. Appl Math Lett, 2010, 23(5):581-584.
[13] MA Ruyun, CHEN Ruipeng, CHEN Tianlan. Existence of positive periodic solutions of nonlinear first order delayed differential equations[J]. J Math Anal Appl, 2011, 384(2):527-535.
[14] YAN Jurang. Existence of positive periodic solutions of impulsive functional differential equations with two parameters[J]. J Math Anal Appl, 2007, 327(2):854-868.
[15] LI Yongkun, FAN Xuanlong, ZHAN Lili. Positive periodic solutions of functional differential equations with impulses and a parameter[J]. Comput Math Appl, 2008, 56(10):2556-2560.
[16] LI Xiaoyue, LIN Xiaoning, JIANG Daqing. Existence and multiplicity of positive periodic solutions to functional differential equations with impulses effecta[J]. Nonlinear Anal, 2005, 62(4):683-701.
[17] LI Jianli, SHEN Jianhua. Existence of positive periodic solutions to a class of functional differential equations with impulse[J]. Math Appl, 2004, 17(3):456-463.
[18] YAN Jurang. Existence and global attractivity of positive periodic solutions for an impulsive Lasota-Wazewska model[J]. J Math Anal Appl, 2003, 279(1):111-120.
[1] 闫东亮. 带有导数项的二阶周期问题正解[J]. 山东大学学报（理学版）, 2017, 52(9): 69-75.
[2] 何志乾, 苗亮英. 带弱奇性的二阶阻尼微分方程正周期解的存在性[J]. 山东大学学报（理学版）, 2017, 52(10): 84-88.
[3] 王双明. 一类具有时滞的周期流行病模型的动力学分析[J]. 山东大学学报（理学版）, 2017, 52(1): 81-87.
[4] 陈彬. 格林函数变号的三阶周期边值问题[J]. 山东大学学报（理学版）, 2016, 51(8): 79-83.
[5] 郭丽君. 非线性微分方程三阶三点边值问题正解的存在性[J]. 山东大学学报（理学版）, 2016, 51(12): 47-53.
[6] 吴成明. 二阶奇异耦合系统正周期解的存在性[J]. 山东大学学报（理学版）, 2015, 50(10): 81-88.
[7] 黄翠,王彩侠, 宋晓秋*,张明翠. 双参数C-半群及其应用[J]. J4, 2013, 48(10): 14-17.
[8] 胡兵,乔元华*. 具有脉冲积分条件的泛函微分方程解的存在性和二阶收敛性[J]. J4, 2012, 47(6): 20-27.
[9] 卢芳,周宗福*. 一类具p-Laplacian算子四阶奇异边值问题正解的存在性[J]. J4, 2012, 47(6): 28-33.
[10] 杨春风. 一类三阶三点边值问题正解的存在性和不存在性[J]. J4, 2012, 47(10): 109-115.
[11] 姚林红1, 赵爱民2. 非线性项变号的脉冲微分方程正解的存在性[J]. J4, 2010, 45(12): 83-87.
[12] 刘树宽. 奇异二阶Neumann边值问题的多解性[J]. J4, 2010, 45(10): 98-103.
[13] . pLaplacian边值问题的多重正解[J]. J4, 2009, 44(7): 79-82.
[14] 陈祥平,李仁贵. 超线性奇异脉冲微分方程的正解[J]. J4, 2009, 44(3): 45-49 .
[15] 俎冠兴. 边值问题的多重正解[J]. J4, 2009, 44(12): 71-76.
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
版权所有 © 2018 《山东大学学报(理学版)》编辑部　
地址: 山东省济南市山大南路27号山东大学中心校区（250100）　电话: +86-0531-88366917　E-mail: xblxb@sdu.edu.cn
本系统由北京玛格泰克科技发展有限公司设计开发