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《山东大学学报(理学版)》 ›› 2019, Vol. 54 ›› Issue (12): 38-45.doi: 10.6040/j.issn.1671-9352.0.2019.461

• • 上一篇    

一类奇异二阶阻尼差分方程周期边值问题正解的存在性

苏肖肖   

  1. 西北师范大学数学与统计学院, 甘肃 兰州 730070
  • 发布日期:2019-12-11
  • 作者简介:苏肖肖(1995— ), 女, 硕士研究生, 研究方向为常微分方程边值问题. E-mail:suxiaoxiao2856@163.com
  • 基金资助:
    国家自然科学基金资助项目(11671322)

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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摘要： 研究了一类奇异二阶阻尼差分方程周期边值问题{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)正解的存在性,其中T >2是一个整数, α、 β均为常数, f(t,x,y):［1,T］Z×(0,∞)×R→R关于(x,y)∈(0,∞)×R连续且允许f在x=0处奇异即limx→0+ f(t,x,y)=+∞,(t,y)∈［1,T］Z×R。主要结果的证明基于Leray-Schauder非线性抉择。

关键词: 差分方程, 正解, 奇异性, 格林函数, Leray-Schauder非线性抉择

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

中图分类号: 

  • O175.8
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