浙江大学学报（理学版）2026，Vol.53Issue(4)：454-463,10.DOI:10.3785/1008-9497.25090
Minkowski空间带平均曲率算子的离散Robin系统正解的存在性和多重性
Existence and multiplicity of positive solutions for a discrete Robin system involving the mean curvature operator in Minkowski space
摘要
Abstract
This paper studies the existence,multiplicity and non-existence of positive solutions for a discrete Robin system with the mean curvature operator:{∇[t N-1ϕ(Δu(t))]+tN-1 λ1 μ1(t)f1(u,v)=0,t∈[1,n-1]Z,∇[t N-1ϕ(Δv(t))]+tN-1 λ2 μ2(t)f2(u,v)=0,t∈[1,n-1]Z,Δu(0)=u(n)=0=v(n)=Δv(0),where ϕ(y)=y/√1-y2(y∈R,|y|<1),the parameters λ1,λ2>0,n>3 is a positive integer,N≥2 is a constant,[1,n-1]Z:={1,2,…,n-1},Δ is the forward difference operator,∇ is the backward difference operator,μ1,μ2:[1,n-1]Z →[0,∞)are positive functions and fi:[0,+∞)×[0,+∞)→[0,+∞)is continuous,i=1,2.It is proved that there exists a continuous curve Γ dividing the first quadrant into two disjoint unbounded open sets O1 and O2,such that the system has zero,at least one or at least two positive solutions when(λ1,λ2)belongs to O1,Γ or O2,respectively.关键词
离散Robin系统/平均曲率算子/正解/存在性/多重性Key words
discrete Robin system/mean curvature operator/positive solution/existence/multiplicity分类
数理科学引用本文复制引用
吴承泽,路艳琼..Minkowski空间带平均曲率算子的离散Robin系统正解的存在性和多重性[J].浙江大学学报（理学版）,2026,53(4):454-463,10.基金项目
国家自然科学基金项目(12361040,12461035) （12361040,12461035）
青海省自然科学基金项目(2025-ZJ-722). （2025-ZJ-722）
