一维离散平均曲率方程Neumann问题解的存在性  

Existence of Solutions for Neumann Problem ofOne-Dimensional Discrete Mean Curvature Equation

作　　者：段磊 陈天兰 DUAN Lei;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）》2021年第4期731-736,共6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(批准号:20JR10RA100).

摘　　要：用紧向量场方程的解集连通理论给出一维离散平均曲率方程Neumann问题Δ[ϕ(Δu(t-1))]=f(t,u(t)),t∈[1,T]_(Z),Δu(0)=Δu(T)=0的上下解方法,并给出其解的存在性结果,其中:[1,T]z∶={1,2,…,T-1,T},T≥2是正整数;ϕ(s)=s/√1-s^(2),s∈(-1,1);非线性项f:[1,T]_(z)×R→R连续.By using the connectivity theory of solution sets of compact vector field equation,we give the methods of upper and lower solutions for Neumann problem of one-dimensional discrete mean curvature equationΔ[ϕ(Δu(t-1))]=f(t,u(t)),t∈[1,T]_(Z),Δu(0)=Δu(T)=0,and give the existence result of their solutions,where[1,T]z∶={1,2,…,T-1,T},T≥2 and T∈X^(+),ϕ(s)=s/√1-s^(2),s∈(-1,1),the nonlinear term f:[1,T]_(z)×R→R is continuous.

关 键 词：平均曲率方程 NEUMANN问题 解集连通理论 上下解 

分 类 号：O175.7[理学—数学]