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

TAN Hui-xuan, FENG Han-ying, FENG Xing-fang, DU Ya-tao

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

Chinese Quarterly Journal of Mathematics >

2015 , Vol. 30 >Issue 1: 55 - 65

DOI: https://doi.org/10.13371/j.cnki.chin.q.j.m.2015.01.007

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

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Department of Mathematics, Mechanical Engineering College

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.

Received date: 2013-03-28

Online published: 2020-11-24

Supported by

Supported by the HEBNSF of China(A2012506010)； Supported by the YSF of Heibei Province(A2014506016)；

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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

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

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