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Existence of positive solution for discrete prescribed mean curvature four-point boundary value problems
- LI Zhiqiang, LU Yanqiong
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2025, 60(5):
40-49.
doi:10.6040/j.issn.1671-9352.0.2023.548
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By using the fixed point theorem, we establish the existence and multiplicity of(positive)solutions for the following discrete four-point boundary value problem with one-dimension Minkowski mean curvature operator{-(Δφ(Δu(k-1)))=f(k,u(k),Δu(k)), k∈[1,N]Z,u(0)=αu(l1), u(N+1)=βu(l2),where f:[1,N]Z×R×R→R is continuous, α, β∈[0,1)are constants and α≠β, l1,l2∈[1,N]Z, l1<l2, φ:(-a,a)→R(0<a<∞)is a monotonic increasing operator and φ(s)=s/((1-s2)1/2), [1,N]Z={1,2,3,…,N}, N≥6.