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

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.