带阻尼项的二阶差分方程周期边值问题正解的存在性  

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

作　　者：苏肖肖 张亚莉 SU Xiao-xiao;ZHANG Ya-li(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu,China)

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2021年第2期56-63,共8页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11671322);西北师范大学研究生科研资助项目(2019KYZZ012034)。

摘　　要：研究了格林函数非负时带阻尼项的二阶差分方程周期边值问题{Δ^(2)x(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)正解的存在性,其中T> 2是一个整数,p(·)、q(·)均为函数,f(t,x,y):[1,T]Z×(0,∞)×R→R关于(x,y)∈(0,∞)×R连续。主要结果的证明基于Leray-Schauder非线性抉择和Schauder不动点定理。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.

关 键 词：差分方程 正解 阻尼项 非负格林函数 LERAY-SCHAUDER非线性抉择 

分 类 号：O175.7[理学—数学] O175.8[理学—基础数学]