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LI Xian, DA Juxia, ZHANG Huan. The Existence of n Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(1): 123-127. DOI: 10.6054/j.jscnun.2024015
Citation: LI Xian, DA Juxia, ZHANG Huan. The Existence of n Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China Normal University (Natural Science Edition), 2024, 56(1): 123-127. DOI: 10.6054/j.jscnun.2024015

The Existence of n Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem

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  • Received Date: January 09, 2023
  • Available Online: April 29, 2024
  • Applying of the monotone iterative technique, the existence of positive solutions to the fourth-order boundary value problem is studied: u(4)(t)=f(u(t))(t?[0,1]),u(0)=u(1)=0,u(0)=u(1)=0. The above boundary value problem has n symmetric positive solutions under certain conditions.
  • [1]
    达举霞. 四阶两点边值问题3个对称正解的存在性[J]. 华南师范大学学报(自然科学版), 2021, 53(1): 90-93. doi: 10.6054/j.jscnun.2021014

    DA J X. The existence of three symmetric positive solutions to a fourth-order two-point boundary value problems[J]. Journal of South China Normal University (Natural Science Edition), 2021, 53(1): 90-93. doi: 10.6054/j.jscnun.2021014
    [2]
    达举霞, 韩晓玲. 奇异四阶三点边值问题正解的存在性[J]. 四川大学学报(自然科学版), 2017, 54(3): 441-447. https://www.cnki.com.cn/Article/CJFDTOTAL-SCDX201703001.htm

    DA J X, HAN X L. Positive solutions of singular fourth-order three-point boundary value problem[J]. Journal of Sichuan University (Natural Science Edition), 2017, 54(3): 441-447. https://www.cnki.com.cn/Article/CJFDTOTAL-SCDX201703001.htm
    [3]
    MINGHE P, SUNG K C. Monotone iterative technique and symmetric positive solutions for a fourth-order boundary value problem[J]. Mathematical and Computer Mo-delling, 2010, 51: 1260-1267. doi: 10.1016/j.mcm.2010.01.009
    [4]
    林府标, 杨欣霞, 张千宏. 一类积分-偏微分群体平衡方程的非完全不变群及显式精确解[J]. 华南师范大学学报(自然科学版), 2023, 55(5): 72-79. doi: 10.6054/j.jscnun.2023065

    LIN F B, YANG X X, ZHANG Q H. Incomplete invariant groups and explicit exact solutions of a class of integropartial differential population balance equation[J]. Journal of South China Normal University (Natural Science Edition), 2023, 55(5): 72-79. doi: 10.6054/j.jscnun.2023065
    [5]
    达佳丽, 韩晓玲. 三阶三点边值问题3个正解的存在性[J]. 华南师范大学学报(自然科学版), 2015, 47(3): 148-150. https://www.cnki.com.cn/Article/CJFDTOTAL-HNSF201503026.htm

    DA J L, HAN X L. The existence of three positive solutions of third-order three-point boundary value problem[J]. Journal of South China Normal University (Natural Science Edition), 2015, 47(3): 148-150. https://www.cnki.com.cn/Article/CJFDTOTAL-HNSF201503026.htm
    [6]
    陈剑, 曾泰山. 时间分数阶次扩散方程的多层扩充算法[J]. 华南师范大学学报(自然科学版), 2020, 52(3): 106-110. doi: 10.6054/j.jscnun.2020051

    CHEN J, ZENG T S. Multi-layer extended algorithm for time fractional diffusion equation[J]. Journal of South China Normal University (Natural Science Edition), 2020, 52(3): 106-110. doi: 10.6054/j.jscnun.2020051
    [7]
    达举霞, 霍梅, 韩晓玲. 带变号格林函数的四阶三点边值问题的多个正解的存在性[J]. 华南师范大学学报(自然科学版), 2017, 49(3): 109-113. http://journal-n.scnu.edu.cn/cn/article/id/3845

    DA J X, HUO M, HAN X L. The existence of multiple positive solutions to fourth-order three-point boundary value problems with changing sign Green's founction[J]. Journal of South China Normal University (Natural Science Edition), 2017, 49(3): 109-113. http://journal-n.scnu.edu.cn/cn/article/id/3845
    [8]
    LI Y K, WANG L Y. Multiple positives solutions of nonlinear third-order boundary value problems with integral boundary conditions on times scales[J]. Advances in Difference Equations, 2015, 90: 1-8.
    [9]
    PALAMIDES A P, SMYRLIS G. Positive solutions to a singular third-order three-point boundary value problem with an indefinitely signed Green's function[J]. Nonlinear Analysis, 2008, 68(1): 2014-2118.
    [10]
    ZHOU Y L, ZHANG X M. Triple positive solutions of fourth-order impulsive differential equations with integral boundary conditions[J]. Boundary Value Problems, 2015, 2015: 2/1-14.
    [11]
    WANG Y. Existence of multiple positive solutions for one-dimensional p-Laplacian[J]. Journal of Mathematical Analysis and Applications, 2006, 315: 144-153.
    [12]
    LIU Y J. Picard boundary value problems of second order p-Laplacian differential equations[J]. Chinese Quarterly Journal of Mathematics, 2011, 26(1): 77-84.
    [13]
    WU H Y, ZHANG J H. Positive solutions of higher-order four-point boundary value problem with Laplacian operator[J]. Journal of Computational and Applied Mathema-tics, 2010, 233(11): 2757-2766.
    [14]
    YANG X J, KIN Y, LO K. Periodic solutions for a generalized p-Laplacian equation[J]. Applied Mathematics Letter, 2012, 25(3): 586-589.
    [15]
    AVERY R I, PETERSON A. Three positive fixed points of nonlinear operators on ordered Banach spaces[J]. Computers & Mathematics with Applications, 2001, 42(3/4/5): 313-322.
    [16]
    AVERY R I. A generalization of the Leggett-Williams fixed-point theorem[J]. Mathematical Sciences Research Hot-Line, 1999, 3(7): 9-14.

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