一类带变号权函数的二阶差分方程Dirichlet边值问题正解的存在性  

Existence of positive solutions for a class of second-order difference equation Dirichlet boundary problems with sign-changing weight function

作　　者：张亚莉 ZHANG Ya-Li(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《四川大学学报（自然科学版）》2020年第3期455-458,共4页Journal of Sichuan University(Natural Science Edition)

基　　金：国家自然科学基金(11671322)。

摘　　要：本文研究了非线性二阶差分方程Dirichlet边值问题Δ~2u(t-1)+λa(t)f(u(t))=0,t∈[1,T]_Z,u(0)=u(T+1)=0正解的存在性,其中Δu(t-1)=u(t)-u(t-1),T>2是一个整数,λ是一个正参数,f:■连续且f(0)>0,权函数a:■允许变号.主要结果的证明基于Leray-Schauder不动点定理.In this paper, we study the existence of positive solutions for the nonlinear second-order difference equation Dirichlet boundary problems Δ~2u(t-1)+λa(t)f(u(t))=0, t∈[1, T]_Z,u(0)=u(T+1)=0,where Δu(t-1)=u(t)-u(t-1),T>2 is an integer,λ is a positive parameter,f:■ is continuous, f(0)>0 and a:■ may change sign.The proof of the main results is based on the Leray-Schauder fixed point theorem.

关 键 词：差分方程 变号权函数 LERAY-SCHAUDER不动点定理 正解 

分 类 号：O175.8[理学—数学]