带平均曲率算子的离散混合边值问题凸解的存在性  

Existence of Convex Solutions for a Discrete Mixed Boundary Value Problem with the Mean Curvature Operator

作　　者：段磊 陈天兰 Duan Lei;Chen Tianlan(College of Mathematics and Statistics,Northwest Normal University,Lanzhou 730070)

机构地区：[1]西北师范大学数学与统计学院,兰州730070

出　　处：《数学物理学报（A辑）》2022年第2期379-386,共8页Acta Mathematica Scientia

基　　金：国家自然科学基金(11801453,11901464);甘肃省青年科技基金(20JR10RA100)。

摘　　要：运用锥上的不动点定理讨论了Minkowski空间平均曲率算子的离散混合边值问题Δ[Φ(Δv(t-1))]=f(t,-v(t)),t∈[2,T-1]z,Δv(1)=0,v(T)=0非平凡凸解的存在性,其中Φ(s)=s/√1-x^(2),s∈(-1,1),[2,T-1]z:={2,3,……T-2,T-1},T≥4是正整数,非线性项f(t,u)非负连续,在u=1处允许具有奇异性.In this paper,by using the fixed point theorem in cones,we discuss the existence of Δ[Φ(Δv(t-1))]=f(t,-v(t)),t∈[2,T-1]_(Z),Δv(1)=0,v(T)=0 nontrivial convex solutions for a discrete mixed boundary value problem of mean curvature operator in Minkowski space,where Φ(s)=s/√1-x^(2),s∈(-1,1),[2,T-1]z:={2,3,……T-2,T-1},T≥4 and T∈N*,the nonlinear term f(t,u)is nonnegative and continuous,and singularity is allowed at u=1.

关 键 词：平均曲率算子 离散混合边值问题 非平凡凸解 锥 不动点定理 

分 类 号：O175.7[理学—数学]