JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2015, Vol. 50 ›› Issue (06): 69-74.doi: 10.6040/j.issn.1671-9352.0.2014.585

Previous Articles     Next Articles

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

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

CLC Number: 

  • 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] YAN Dong-liang. Positive solutions of a second order periodic problems with derivative terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(9): 69-75.
[2] . Periodic solutions for second order singular damped differential equations with a weak singularity [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(10): 84-88.
[3] WANG Shuang-ming. Dynamical analysis of a class of periodic epidemic model with delay [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2017, 52(1): 81-87.
[4] GUO Li-jun. Existence of positive solutions for a third-order three-point boundary value problem of nonlinear differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2016, 51(12): 47-53.
[5] WU Cheng-ming. Existence of positive periodic solutions for second order singular coupled systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2015, 50(10): 81-88.
[6] YANG Chun-feng. Existence and nonexistence of positive solutions for a  third-order three-point boundary value problem [J]. J4, 2012, 47(10): 109-115.
[7] YAO Lin-hong1, ZHAO Ai-min2. Existence of positive solutions for an impulsive differential equation with a sign changing nonlinear term [J]. J4, 2010, 45(12): 83-87.
[8] LIU Shu-kuan. Existence of multiple positive solutions for singular second order  Neumann boundary value problems [J]. J4, 2010, 45(10): 98-103.
[9] . Multiple positive solutions for pLaplacian boundar y value problems [J]. J4, 2009, 44(7): 79-82.
[10] CHEN Xiangping, LI Rengui. [J]. J4, 2009, 44(3): 45-49 .
[11] ZHANG Xing-qiu,WANG Shao-feng . The positive solution and multiplicity for second order differential [J]. J4, 2006, 41(4): 4-07 .
Viewed
Full text


Abstract

Cited
  Shared   
  Discussed   
No Suggested Reading articles found!
Copyright 2018 © Editorial office of JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
Supported by Beijing Magtech Co.Ltd