JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2019, Vol. 54 ›› Issue (12): 38-45.doi: 10.6040/j.issn.1671-9352.0.2019.461

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Existence of positive solutions for periodic boundary conditions of singular second-order damped difference equations

SU Xiao-xiao   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2019-12-11

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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)+αΔx(t-1)+βx(t)=f(t,x(t), Δx(t-1)), t∈［1,T］Z,x(0)=x(T), Δx(0)=Δx(T)where T >2 is an integer, α, β are constants, f(t,x,y):［1,T］Z×(0,∞)×R→R is continuous with respect to (x,y)∈(0,∞)×R, f may be singular at x=0, which means that limx→0+ f(t,x,y)=+∞,(t,y)∈［1,T］Z×R. The proof of main results is based on nonlinear alternative of Leray-Schauder.

Key words: difference equation, positive solution, singular, Greens function, nonlinear alternative of Leray-Schauder

CLC Number: 

  • O175.8
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