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OA

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.