带非线性边界条件的一类离散梁方程正解的存在性  

Existence of Positive Solutions for a Class of DiscreteBeam Equations with Nonlinear Boundary Conditions

作　　者：景证棋 路艳琼 JING Zhengqi;LU Yanqiong(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070,China)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《吉林大学学报（理学版）》2022年第4期767-774,共8页Journal of Jilin University:Science Edition

基　　金：国家自然科学基金青年科学基金(批准号:11901464,11801453).

摘　　要：用Krasnoselskii不动点定理给出带非线性边界条件的一类离散梁方程{Δ^(4)u(t-2)=λh(t)f(u(t)),t∈[2,T]_(z),u(0)=Δu(0)=0,Δ^(2)u(T)=0,Δ^(3)u(T-1)+c(u(T))u(T)=0正解的存在性结果,其中:λ>0为参数;h:[2,T]_(z)→[0,∞)为函数;f:(0,∞)→ℝ连续且在u=0处允许有奇性,在u=∞处超线性增长.By using the fixed-point theorem of Krasnoselskii,we give the existence of positive solutions[JP]for a class of discrete beam equations with nonlinear boundary conditions {Δ^(4)u(t-2)=λh(t)f(u(t)),t∈[2,T]_(z),u(0)=Δu(0)=0,Δ^(2)u(T)=0,Δ^(3)u(T-1)+c(u(T))u(T)=0,where λ>0 is a parameter,h:[2,T]_(z)→[0,∞)is function,f:(0,∞)→ℝis continuous,and allows singularity at u=0,grows superlinearly at u=∞.

关 键 词：非线性边界条件 正解 LEBESGUE控制收敛定理 超线性增长 

分 类 号：O175.8[理学—数学]