JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2021, Vol. 56 ›› Issue (2): 56-63.doi: 10.6040/j.issn.1671-9352.0.2020.361

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Existence of positive solutions for periodic boundary value problems of secondorder damped difference equations

SU Xiao-xiao, ZHANG Ya-li   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Online:2021-02-20 Published:2021-01-21

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Abstract: This paper studies the existence of positive solutions for periodic boundary value problems of second order damped difference equations{Δ2x(t-1)+p(t)Δx(t-1)+q(t)x(t)=f(t,x(t),Δx(t-1)), t∈［1,T］Z, x(0)=x(T), Δx(0)=Δx(T)with vanishing Greens function, where T > 2 is a integer, p(·),q(·) are functions, f(t,x,y):［1,T］Z×(0,∞)×R→R is continuous with respect to (x,y)∈(0,∞)×R. The proof of main results is based on nonlinear alternative of Leray-Schauder and Schauders fixed point theorem.

Key words: difference equation, positive solution, damped term, nonnegative Greens function, nonlinear alternative of Leray-Schauder

CLC Number: 

  • O175.7
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