渐近线性二阶半正离散边值问题正解的分歧结构

Bifurcation structure of asymptotically linear second-order semipositone discrete boundary value problem

在非线性项满足渐近线性增长条件下,研究了二阶半正离散边值问题{-Δ2u(t-1)=λf(t,u(t)),t∈[1,T]Z,αu(0)-βΔu(0)=0,γu(T)+δΔu(T)=0正解的存在性,其中λ>0为参数,f:[1,T]Z×R+→R连续,主要结果的证明基于分歧理论及拓扑度理论。

It is studied that the existence of positive solutions of second-order semipositone discrete boundary value problem with the nonlinearity satisfies asymptotically linear conditions,-Δ2u（t-1） =λf（t,u（t））, t∈[1,T]Z,αu（0） -βΔu（0） =0,γu（T） ＋δΔu（T） =0,{where λ is a positive parameter, f：[1,T] Z × R＋→R is continuous, The proofs of the main results are based on the to-pological degree techniques and bifurcation theory.