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

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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

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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
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