JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE) ›› 2025, Vol. 60 ›› Issue (5): 40-49.doi: 10.6040/j.issn.1671-9352.0.2023.548

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Existence of positive solution for discrete prescribed mean curvature four-point boundary value problems

LI Zhiqiang, LU Yanqiong*   

  1. College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, Gansu, China
  • Published:2025-05-19

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Abstract: 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, l12, φ:(-a,a)→R(02)1/2), ［1,N］Z={1,2,3,…,N}, N≥6.

Key words: Minkowski mean curvature operator, positive solution, multiplicity, fixed point theorem

CLC Number: 

  • O175.8
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