一类二阶差分方程组Dirichlet边值问题的正解  

Positive Solutions of Dirichlet Boundary Value Problems for a Class of Second-Order Difference Equations

作　　者：吴海艺 陈天兰 WU Haiyi;CHEN Tianlan(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）》2023年第2期214-220,共7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:11801453,11901464)、甘肃省青年科技基金计划项目(批准号:20JR10RA100);甘肃省高等学校创新能力提升项目(批准号:2021A-006);2022年度甘肃省教育厅高等学校创新基金(批准号:2022A-218).

摘　　要：用非负上凸函数的Jensen不等式和不动点指数理论讨论一类非线性差分方程组边值问题正解的存在性,得到了二阶差分方程组Dirichlet边值问题-Δ^(2)u(t-1)=f(t,u,v),t∈[1,T],-Δ^(2)v(t-1)=g(t,u,v),t∈[1,T],u(0)=u(T+1)=0,v(0)=v(T+1)=0正解存在的充分条件,其中[1,T]∶={1,2,…,T},T≥2是一个整数;Δu(t)=u(t+1)-u(t)为前向差分算子;f,g:[1,T]×[0,∞)×[0,∞)→[0,∞)连续.Abstract:By using Jensen’s inequality of nonnegative upper convex function and the fixed point index theory,we discuss the existence of positive solutions of the boundary value problem for a class of nonlinear difference equations,and obtain sufficient conditions for the existence of positive solutions of the Dirichlet boundary value problem for the second order difference equations-Δ^(2)u(t-1)=f(t,u,v),t∈[1,T],-Δ^(2)v(t-1)=g(t,u,v),t∈[1,T],u(0)=u(T+1)=0,v(0)=v(T+1)=0,where[1,T]∶={1,2,…,T},T≥2 is the integer,Δu(t)=u(t+1)-u(t)is the forward difference operator,f,g:[1,T]×[0,∞)×[0,∞)→[0,∞)are continuous.

关 键 词：JENSEN不等式 正解 二阶差分方程组 不动点指数理论 

分 类 号：O175.7[理学—数学]