带阻尼项的二阶差分方程周期边值问题正解的存在性

doi:10.6040/j.issn.1671-9352.0.2020.361

摘要/Abstract

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{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)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。

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

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

中图分类号:

O175.7

苏肖肖, 张亚莉. 带阻尼项的二阶差分方程周期边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2021, 56(2): 56-63.

SU Xiao-xiao, ZHANG Ya-li. Existence of positive solutions for periodic boundary value problems of secondorder damped difference equations[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2021, 56(2): 56-63.

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