带p-Laplacian算子的三阶三点边值问题的三个正解

doi:10.13371/j.cnki.chin.q.j.m.2015.01.007

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

带p-Laplacian算子的三阶三点边值问题的三个正解

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

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/Abstract

摘要： In this paper, we consider the three-point boundary value problem \phi_p（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 \phi_p（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, fixed point theorem

Abstract: In this paper, we consider the three-point boundary value problem \phi_p（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 \phi_p（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, fixed point theorem

中图分类号:

O175.8

谭惠轩, 封汉颍, 冯杏芳, 杜亚涛. 带p-Laplacian算子的三阶三点边值问题的三个正解[J]. 数学季刊, 2015, 30(1): 55-65.

TAN Hui-xuan, FENG Han-ying, FENG Xing-fang, DU Ya-tao. Triple Positive Solutions to a Third-order Three-point Boundary Value Problem with p-Laplacian Operator[J]. Chinese Quarterly Journal of Mathematics, 2015, 30(1): 55-65.

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带p-Laplacian算子的三阶三点边值问题的三个正解

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

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