留言板

尊敬的读者、作者、审稿人, 关于本刊的投稿、审稿、编辑和出版的任何问题, 您可以本页添加留言。我们将尽快给您答复。谢谢您的支持!

姓名
邮箱
手机号码
标题
留言内容
验证码

四阶两点边值问题3个对称正解的存在性

达举霞

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
引用本文: 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 Juxia. The Existence of Three Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(1): 90-93. doi: 10.6054/j.jscnun.2021014
Citation: DA Juxia. The Existence of Three Symmetric Positive Solutions to A Fourth-Order Two-Point Boundary Value Problem[J]. Journal of South China normal University (Natural Science Edition), 2021, 53(1): 90-93. doi: 10.6054/j.jscnun.2021014

四阶两点边值问题3个对称正解的存在性

doi: 10.6054/j.jscnun.2021014
基金项目: 

国家自然科学基金项目 11561063

详细信息
    通讯作者:

    达举霞, Email: 1414320179@qq.com

  • 中图分类号: O175.8

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

  • 摘要: 应用广义的Leggett-Williams不动点定理,研究了四阶两点边值问题 $ {{u}^{\left( 4 \right)}}\left( t \right)=f\left( u\left( t \right) \right)\ \ \ \ \ \left( t\in \left[ 0, 1 \right] \right), u\left( 0 \right)=u\left( 1 \right)=0, {u}''\left( 0 \right)={u}''\left( 1 \right)=0 $ 正解的存在性, 其中$f:\mathbb{R}\to \left[ 0, +\infty \right)$连续. 在f满足适当的增长条件下, 得到该问题至少存在3个对称正解.
  • [1] 周韶林, 吴红萍, 韩晓玲. 一类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), 2014, 51(1): 11-15. https://www.cnki.com.cn/Article/CJFDTOTAL-SCDX201401003.htm

    ZHOU S L, WU H P, HAN X L. Existence of positive solutions of the fourth-order three-point boundary value problems[J]. Journal of Sichuan University(Natural Science Edition), 2014, 51(1): 11-15. https://www.cnki.com.cn/Article/CJFDTOTAL-SCDX201401003.htm
    [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. doi: 10.3969/j.issn.0490-6756.2017.03.001

    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. doi: 10.3969/j.issn.0490-6756.2017.03.001
    [3] AVERY R I, HENDERSON J. Three symmetric positive solutions for a second-order boundary value problem[J]. Applied Mathematics Letters, 2000, 13: 1-7. http://www.sciencedirect.com/science/article/pii/S0893965999001779
    [4] 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. http://journal-n.scnu.edu.cn/article/id/3437

    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. http://journal-n.scnu.edu.cn/article/id/3437
    [5] 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
    [6] 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/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/article/id/3845
    [7] 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. doi: 10.1186/s13662-015-0442-6
    [8] PALAMIDES A P, GEORGE S. Positive solutions to a singular third-order three-point boundary value problem with an indefinitely signed Green's function[J]. Nonlinear Analysis, 2008, 68: 2014-2019.
    [9] ZHOU Y L, ZHANG X M. Existence of positive solutoins of fourth-order ompulsive differential equations with integral boundary condition[J]. Nonlinear Analysis, 2015, 2: 1-6.
    [10] WANG Y. Existence of multiple positive solutions for one-dimensional p-Laplacian[J]. Journal of Mathematical Analysis and Applications, 2006, 315: 144-153. doi: 10.1016/j.jmaa.2005.09.085
    [11] 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. http://www.cqvip.com/QK/97306X/201101/37879789.html
    [12] 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. doi: 10.1016/j.cam.2009.06.040
    [13] YANG X J, KIN Y, LO K. Periodic solutions for a gene-ralized p-Laplacian equation[J]. Applied Mathematics Letter, 2012, 25(3): 586-589. doi: 10.1016/j.aml.2011.09.064
    [14] AVERY R I, PETERSON A. Three positive fixed points of nonlinear operators on ordered Banach spaces[J]. Computers#38;Mathematics with Applications, 2001, 42(3/4/5): 313-322. http://www.ams.org/mathscinet-getitem?mr=542951
    [15] ZHAO J, MIAO C, GE W, et al. Multiple symmetric positive solutions to a new kind four point boundary value problem[J]. Nonlinear Analysis, 2009, 71: 9-18. http://www.ams.org/mathscinet-getitem?mr=2518007
    [16] AVERY R I. A generalization of the Leggett-Williams fixed-point theorem[J]. Mathematical Science Research Hot-Line, 1999, 3(7): 9-14. http://www.ams.org/mathscinet-getitem?mr=1702612
  • 加载中
计量
  • 文章访问数:  315
  • HTML全文浏览量:  95
  • PDF下载量:  36
  • 被引次数: 0
出版历程
  • 收稿日期:  2020-05-08
  • 网络出版日期:  2021-03-24
  • 刊出日期:  2021-02-25

目录

    /

    返回文章
    返回