格林函数变号时二阶离散周期边值问题正解的存在性  

Existence of positive solutions for second order discrete periodic boundary value problems with sign-changing Green’s function

作　　者：胡文丰 王晶晶 HU Wenfeng;WANG Jingjing(Department of Public Course Teaching,Ningbo Polytechnic,Ningbo 315800,Zhejiang Province,China;College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]宁波职业技术学院公共教学部,浙江宁波315800 [2]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《浙江大学学报（理学版）》2022年第6期670-675,共6页Journal of Zhejiang University（Science Edition）

基　　金：宁波职业技术学院校级课题(NZ22013)。

摘　　要：运用锥上的不动点指数理论,讨论了格林函数变号时的二阶离散周期边值问题{Δ^(2)u(t-1)+k^(2)u(t)=λb(t)f(u(t)),t∈[1,n]_(z),u(0)=u(n),Δu(0)=Δu(n).当λb(t)≡1时,该问题存在正解;当b:[1,n]→R^(+)时,该问题不存在正解,其中f∈C (R^(+),R^(+)),k为满足tanθ=k√4-k^(2)/2-k^(2)的常数,λ为参数,θ∈(0,3π/2n],R^(+):=[0,∞).In this paper, the second order discrete periodic boundary value problem {Δ^(2)u(t-1)+k^(2)u(t)=λb(t)f(u(t)),t∈[1,n]_(z),u(0)=u(n),Δu(0)=Δu(n) is studied by using the fixed point index theory on the cone. Firstly,the existence of the positive solution is proved when λb (t)≡ 1;Secondly, we show the nonexistence of the positive solution of this problem when b:[1,n]Z→ R,where is f ∈ C( R, R),k is a constant satisfying tanθ=k√4-k^(2)/2-k^(2) ,λ is a parameter and θ∈(0,3π/2n],R^(+):=[0,∞).

关 键 词：周期边值问题 正解 变号格林函数 不动点指数 

分 类 号：O175.8[理学—数学]