离散给定平均曲率四点边值问题正解的存在性

doi:10.6040/j.issn.1671-9352.0.2023.548

摘要/Abstract

摘要： 运用不动点定理建立带一维Minkowski平均曲率算子的离散四点边值问题{-(Δφ(Δu(k-1)))=f(k,u(k),Δu(k)),k∈［1,N］_Z,u(0)=αu(l₁), u(N+1)=βu(l₂)(正)解的存在性和多解性, 其中, f:［1,N］_Z×R×R→R为连续函数,α, β∈［0,1)且α≠β为常数,l₁,l₂∈［1,N］_Z且l₁2, φ:(-a,a)→R(02)^1/2), ［1,N］_Z={1,2,…,N}, N≥6为给定的正整数。

关键词: Minkowski平均曲率算子, 正解, 多解性, 不动点定理

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

中图分类号:

O175.8

李志强,路艳琼. 离散给定平均曲率四点边值问题正解的存在性[J]. 《山东大学学报(理学版)》, 2025, 60(5): 40-49.

LI Zhiqiang, LU Yanqiong. Existence of positive solution for discrete prescribed mean curvature four-point boundary value problems[J]. JOURNAL OF SHANDONG UNIVERSITY(NATURAL SCIENCE), 2025, 60(5): 40-49.

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