JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (9): 50-58.doi: 10.6040/j.issn.1671-9352.0.2020.394

Previous Articles     Next Articles

Existence and multiplicity of positive periodic solutions for a class of nonlinear third-order difference equations

ZHAO Jiao   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2021-09-13

PDF (PC)

720

Abstract: This paper considers the existence and multiplicity of positive periodic solutions for a class of nonlinear third-order difference equationΔ3u(t-3)+αΔ2u(t-2)+βΔu(t-1)=f(t,u(t)), t∈［3,T］Z,where T>4, α>0, -1<β<0, f:［3,T］Z×［0,∞)→R is continuous with respect to u∈［0,∞), f(t+ω,u)=f(t,u), ω∈Z+. The proof of the main results is based on Guo-Krasnoselskii fixed point theorem.

Key words: third-order, difference equation, cone, positive periodic solution

CLC Number: 

  • O175.7
[1] MA Ruyun. Multiplicity results for a third order boundary value problem at resonance[J]. Nonlinear Analysis, 1998, 32(4):493-499.
[2] 郝兆才. 半线性三阶差分方程边值问题的非负解[J]. 数学物理学报, 2001, 21(2):225-229. HAO Zhaocai. Nonnegtive solutions for semilinear third-order difference equation boundary value problems[J]. Acta Mathematiea Scientia, 2001, 21(2):225-229.
[3] GENG Tianmei, GAO Chenghua. Positive solutions of discrete third-order boundary value problems with sign-changing Greens function[J]. Advances in Difference Equations, 2016, 110(1):1-13.
[4] FENG Yuqiang. On the existence and multiplicity of positive periodic solutions of a nonlinear third-order equation[J]. Applied Mathematics Letters, 2009, 22(8):1220-1224.
[5] BAI Zhanbing. Existence of solutions for some third-order boundary value problems[J]. Electronic Journal of Differential Equations, 2008, 25(6):359-370.
[6] ALBERTO C, FELIZ M. Existence, non-existence and multiplicity results for a third-order eigenvalue three point boundary value problem[J]. Journal of Nonlinear Sciences and Applications, 2017, 2017(10):5445-5463.
[7] SUN Yongping. Positive solutions for third-order three-point nonhomogeneous boundary value problems[J]. Applied Mathematics Letters, 2009, 22(1):45-51.
[8] ZHANG Rui. Positive solutions of BVPs for third-order discrete nonlinear difference systems[J]. Journal of Applied Mathematics Computing, 2011, 35(1):551-575.
[9] AGARWAL R P, HENDERSON J. Positive solutions and nonlinear problems for third order difference equations[J]. Computers Mathematics with Applications, 1998, 36(10):347-355.
[10] NEMAT N. Existence of three positive solutions for a system of nonlinear third-order ordinary differential equations[J]. Electronic Journal of Differential Equations, 2011, 2011(144):1-7.
[1] Mingxin ZHAO,Guirong SUN,Zhigang HUANG. Entire solutions of differential-difference equation of Fermat type [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(6): 107-112.
[2] QI Huimin, LUO Zhixue. Optimal harvesting for periodic age-structured population dynamics [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(5): 46-52.
[3] WANG Guo-xin, NIU Yu-jun. Real-valued implicit Lagrangian for the stochastic linear second-order cone complementarity problem [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(4): 49-54.
[4] Zijuan ZHOU,Zhixue LUO. Optimal birth control of n species nonlinear competition system with age-structure [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2023, 58(10): 75-83.
[5] YANG Qi. Transcendental solutions of two types of systems of complex differential-difference equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 25-33.
[6] GAO Zhen-guang. Entire solutions of two types of nonlinear differential-difference equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2022, 57(12): 34-44.
[7] SU Xiao-xiao, ZHANG Ya-li. Existence of positive solutions for periodic boundary value problems of secondorder damped difference equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 56-63.
[8] LIU Meng-xue, LI Jie-mei, YAO Yan-yan. Multiplicity of positive solutions for fourth-order boundary value problems with nonlinear boundary conditions [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 84-91.
[9] ZHANG Rui-yan. Existence, nonexistence and multiplicity of positive solutions for a class of nonlinear third order three point boundary value problems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(12): 52-58.
[10] XU Yang, ZHAO Chun. Optimal control of competitive population system with hierarchical structure [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(11): 61-70.
[11] FENG Sheng-yu, CHEN Zi-xu, WANG Deng-xu,. Polysiloxane-based fluorescent materials [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(10): 99-112.
[12] YANG Hu-jun, HAN Xiao-ling. Existence of positive periodic solutions for a class of non-autonomous fourth-order ordinary differential equations [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(6): 109-114.
[13] SUN Yan-yan, LIU Yan-sheng. Existence of positive solutions for singular boundary value problems of Hadamard fractional differential equations in abstract space [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2020, 55(10): 95-103.
[14] CHEN Rui-peng, LI Xiao-ya. Positive periodic solutions for second-order singular differential equations with damping terms [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(8): 33-41.
[15] MA Man-tang. Existence of positive solutions for a class of periodic boundary value problems of nonlinear second-order systems [J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2019, 54(6): 88-95.
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