数学季刊 ›› 2015, Vol. 30 ›› Issue (1): 55-65.doi: 10.13371/j.cnki.chin.q.j.m.2015.01.007

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带p-Laplacian算子的三阶三点边值问题的三个正解

  

  1. Department of Mathematics, Mechanical Engineering College
  • 收稿日期:2013-03-28 出版日期:2015-03-30 发布日期:2020-11-24
  • 作者简介:TAN Hui-xuan(1981-), female, native of Shijiazhuang, Hebei, a lecturer of Mechanical Engineering College, M.S.D., engages in differential equations; FENG Han-ying(1961-), male, native of Fuyang, Anhui, a professor of Mechanical Engineering College, Ph.D., engages in differential equations; FENG Xingfang(1979-), female, native of Xingtai, Hebei, a lecturer of Mechanical Engineering College, M.S.D., engages in differential equations; DU Ya-tao(1977-), female, native of Handan, Hebei, a lecturer of Mechanical Engineering College, Ph.D., engages in differential equations.
  • 基金资助:
    Supported by the HEBNSF of China(A2012506010); Supported by the YSF of Heibei Province(A2014506016);

Triple Positive Solutions to a Third-order Three-point Boundary Value Problem with p-Laplacian Operator

  1. Department of Mathematics, Mechanical Engineering College
  • Received:2013-03-28 Online:2015-03-30 Published:2020-11-24
  • About author:TAN Hui-xuan(1981-), female, native of Shijiazhuang, Hebei, a lecturer of Mechanical Engineering College, M.S.D., engages in differential equations; FENG Han-ying(1961-), male, native of Fuyang, Anhui, a professor of Mechanical Engineering College, Ph.D., engages in differential equations; FENG Xingfang(1979-), female, native of Xingtai, Hebei, a lecturer of Mechanical Engineering College, M.S.D., engages in differential equations; DU Ya-tao(1977-), female, native of Handan, Hebei, a lecturer of Mechanical Engineering College, Ph.D., engages in differential equations.
  • Supported by:
    Supported by the HEBNSF of China(A2012506010); Supported by the YSF of Heibei Province(A2014506016);

摘要: In this paper, we consider the three-point boundary value problem \phip(u′′(t)))′+a(t)f(t, u(t), u′(t), u′′(t)) = 0, t ∈ [0, 1] subject to the boundary conditions u(0) =βu′(0), u′(1) = αu′(η), u′′(0) = 0, where  \phip(s) = |s|p-2s with p > 1, 0 < α, η < 1and 0 ≤β < 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem. 

关键词: third-order three-point boundary value problem, positive solution, fi xed point theorem

Abstract: In this paper, we consider the three-point boundary value problem \phip(u′′(t)))′+a(t)f(t, u(t), u′(t), u′′(t)) = 0, t ∈ [0, 1] subject to the boundary conditions u(0) =βu′(0), u′(1) = αu′(η), u′′(0) = 0, where  \phip(s) = |s|p-2s with p > 1, 0 < α, η < 1and 0 ≤β < 1. Applying a fixed point theorem due to Avery and Peterson, we study the existence of at least three positive solutions to the above boundary value problem. 

Key words: third-order three-point boundary value problem, positive solution, fi xed point theorem

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