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

作　　者：张露[1] 马如云[1] 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2014年第3期79-83,共5页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(11061030)

摘　　要：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.

关 键 词：分歧理论 正解 拓扑度 Sturm-Liouville边界条件 半正问题 

分 类 号：O175.8[理学—数学]