非线性二阶离散周期边值问题的Ambrosetti-Prodi型结果

AMBROSETTI-PRODI TYPE RESULTS FOR NONLINEAR SECOND-ORDER DISCRETE PERIODIC BOUNDARY VALUE PROBLEMS

本文研究了二阶离散周期边值问题{△^(2)u(t-1)+f(t,u(t),△u(t-1))=s,t∈[1,T]z,u(0)-u(T)=△u(0)-△u(T)=0解的个数与参数s的关系,其中f(t,u,v):[1,T]Z×R^(2)→R关于(u,v)∈R^(2)连续,s∈R.利用上下解方法和拓扑度理论,获得了Ambrosetti-Prodi型结果,推广了已有文献的相关结果.

In this paper,we discuss the relationship between the number of the solutions for second-order discrete periodic boundary value problem {△^(2)u(t-1)+f(t,u(t),△u(t-1))=s,t∈[1,T]z,u(0)-u(T)=△u(0)-△u(T)=0 and the parameter s,where f(t,u,v):[1,T]Z×R^(2)→R is continuous with respect to(u,v)∈R^(2),s∈R.By using the method of the upper and lower solutions and topological degree techniques,Ambrosetti-Prodi type result is obtained,and some related conclusions on this topic are general-ized.