中文摘要：

用不动点指数理论,考虑一类非线性二阶差分方程Robin问题{-△~2u（t-1）=λf（u（t））,t∈Z[1,T-1],△u（0）=0,u（T）=0多个正解的存在性,其中：Z[1,T-1]={1,2,…,T-1};f：[0,∞）→[0,∞）为连续函数且有多个零点;λ〉0为参数在一定的假设条件下,讨论其非线性项零点数与问题解数之间的关系.

英文摘要：

Using the fixed point index theory,the author considered the existence of multiple positive solutions for a class of second-order difference equation with Robin problems{-△~2u（t-1）=λf（u（t））,t∈Z[1,T-1],△u（0）=0,u（T）=0where Z[1,T-1]={1,2,…,T-1};f：[0,∞）→[0,∞） is continuous functions with multiple zeros,λ 0 is a parameter.Under certain assumptions,the author discussed the relationship between the nutnber of zeros of nonlinear term and the nutnber of the solutions of the problems.