一类含参数半正二阶离散Neumann边值问题正解的存在性  

Existence of Positive Solution for a Class of Semipositone Second-order Discrete Neumann Boundary Value Problems with a Parameter

作　　者：杨晓梅 路艳琼 YANG Xiaomei;LU Yanqiong(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,Gansu)

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：《四川师范大学学报（自然科学版）》2021年第5期626-630,共5页Journal of Sichuan Normal University（Natural Science）

基　　金：国家自然科学基金青年项目(11801453和11901464)。

摘　　要：基于锥上的不动点定理,获得二阶变系数离散Neumann超线性半正边值问题Δ^(2)u(t-1)+q(t)u(t)=λf(t,u(t)),t∈[1,T]_(Z),{Δu(0)=0,Δu(T)=0正解的存在性与多解性,其中,0≤q(t)<2(1-cosπ/2T),f:[1,T]Z×[0,+∞)→[-M,+∞)连续,[1,T]_(Z):={1,2,…,T},M>0为常数,λ>0为参数.By using the fixed point index theory in cones,we obtain the existence of positive solutions for the superlinear semipositone second-order discrete Neumann boundary value problemΔ^(2)u(t-1)+q(t)u(t)=λf(t,u(t)),t∈[1,T]_(Z),Δu(0)=0,Δu(T)={0 where 0≤q(t)<2(1-cosπ2T),f:[1,T]_(Z)×[0,+∞)→[-M,+∞)is continuous,[1,T]_(Z):={1,2…,T},M is a positive constant,andλis a positive parameter.

关 键 词：NEUMANN边值问题 半正 超线性 不动点定理 

分 类 号：O175.8[理学—数学]