二阶离散p-Laplacian方程Dirichlet边值问题多重正解的存在性

THE EXISTENCE OF MULTIPLE POSITIVE SOLUTIONS OF DIRICHLET BOUNDARY VALUE PROBLEMS FOR SECOND-ORDER P-LAPLACIAN DIFFERENCE EQUATIONS

本文主要讨论了一个满足Dirichlet边界条件的二阶p-Laplacian差分方程正解的存在性.通过利用Leggett-Williams不动点定理的一个推广证明了差分方程△(φ_p(△u(t-1)))+q(t)f(t,u(t))=0,t∈N[1,T]={1,2,…,T}在Dirichlet边界条件u(0)=u(T+1)=0下,当f(t,u)满足一定条件时,至少存在三个正解,这里,φ_p(s)=|s|^(p-2)·s是一个p-Laplacian算子.

In this paper,we mainly consider a second-order p-Laplacian difference equation with Dirichlet boundary value conditions.By using a generalization of the Leggett-Williams fixed-point the- orem due to Avery and Peterson,the existence of at least three positive solutions is established for the following boundary value problem：{△（Фp（△u（t-1）））＋1（t）f（t,u（t））=0,t∈N[1,T],u（0）=u（T＋1）=0