山东大学学报（理学版）
山東大學學報（理學版）
산동대학학보（이학판）
JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE)
2014年
3期
79-83
,共5页
分歧理论%正解%拓扑度%Sturm-Liouville边界条件%半正问题
分歧理論%正解%拓撲度%Sturm-Liouville邊界條件%半正問題
분기이론%정해%탁복도%Sturm-Liouville변계조건%반정문제
bifurcation theory%positive solutions%topological degree%Sturm-Liouville boundary value conditions%semipositone 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。
在非線性項滿足漸近線性增長條件下,研究瞭二階半正離散邊值問題-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為參數, f：[1,T] Z × R+→R連續,主要結果的證明基于分歧理論及拓撲度理論。
재비선성항만족점근선성증장조건하,연구료이계반정리산변치문제-Δ2u(t-1)=λf(t,u(t)), t∈[1,T]Z,αu(0)-βΔu(0)=0,γu(T)+δΔu(T)=0{정해적존재성,기중λ>0위삼수, f：[1,T] Z × R+→R련속,주요결과적증명기우분기이론급탁복도이론。
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.
